P1<''0T. 


A   MANUAL 


OP 


NATURAL  PHILOSOPHY, 


COMPILED  FROM  VARIOUS  SOURCES, 


AND 


DESIGNED  FOR  USE  AS  A  TEXT-BOOK 


IN  HIGH  SCHOOLS  AND  ACADEMIES. 


BY  JOHN  JOHNSTON,  A.M. 

s> 

PROFESSOR  OF  NATURAL  SCIENCE  IN  THE  WESLEYAN   UNIVERSITY 


PHILADELPHIA: 

.THOMAS,   COWPERTHWA1T  &  CO. 
1846. 


Entered,  according  to  Act  of  Congress,  in  the  year  1845,  by 

:    J.O  H  N-  J-O  H  ,N 8  T  O  N  , 
in  the  clerk's  office  oT  the  District  Court 'of  the  District  of  Connecticut. 


JK^^A^J^JBR^HE^PRINTER^ 

(2) 


PREFACE. 


THE  compiler  of  the  following  pages  deems  no  apo- 
logy necessary  for  offering  to  the  public  another  work 
on  Natural  Philosophy.  Of  the  several  works  on  this 
subject  now  before  the  public,  and  with  the  same  gene- 
ral design  as  the  present,  each  one,  no  doubt,  possesses 
its  own  peculiar  excellencies,  and  is  adapted,  more  or 
less,  to  aid  in  advancing  the  great  cause  of  education ; 
but  in  the  multitude  of  seminaries  of  learning,  of  differ- 
ent grades,  in  our  country,  considerable  variety  in  the 
text-books  used  in  them  is  absolutely  necessary.  With- 
out claiming  for  the  present  work,  therefore,  superiority 
in  every  respect  over  others  that  have  appeared  before 
it,  it  is  believed  an  appropriate  place  will  be  found  for 
it,  as  an  assistant  in  promoting  the  cause  of  general 
education. 

As  the  work  professes  to  be  only  a  compilation,  little 
or  nothing  that  is  new  or  original  is,  of  course,  to  be 
expected  in  it ;  but,  while  the  compiler  has  freely  used 
the  works  of  others,  he  has  generally  given  his  own 
illustrations,  seldom  adopting  their  language,  and  never, 
except  when  it  happened  to  accord  perfectly  with  his 

M69909 


IV  PREFACE. 

own  modes  of  thought  and  expression.  This  has  been 
done,  not  from  a  desire  of  being  unlike  others,  but  with 
the  hope  of  being  able  thus  to  condense  more  within  the 
limits  of  the  work,  and  to  preserve  a  greater  uniformity 
of  style.  During  the  preparation  of  the  work,  the  pecu- 
liar wants  of  those  for  whom  it  is  specially  designed 
have  been  constantly  kept  in  mind ;  and  the  writer  is 
not  without  hope,  from  his  long  experience  in  teaching, 
it  may  not  be  found  altogether  unsuited  for  the  use  of 
those  to  whom  it  is  more  especially  offered.  At  the 
same  time  it  is  believed  it  will  be  found  adapted  to 
the  wants  of  such  general  readers  as  are  seeking  solid 
instruction,  rather  than  momentary  gratification. 

In  the  writer's  work  on  Chemistry,  published  seve- 
ral years  since,  the  subjects  of  Heat,  Galvanism,  and 
Electro-Magnetism  are  treated  of  at  length ;  and  it  was, 
therefore,  considered  entirely  unnecessary  to  introduce 
them  into  the  present,  which  is  designed  to  accompany 
the  former,  the  two  together  forming  a  connected  trea- 
tise. It  may,  indeed,  be  objected  that  these  topics  be- 
long rather  to  Natural  Philosophy  than  to  Chemistry; 
but  they  are,  in  fact,  so  intimately  related  to  both  of 
these  branches,  that,  to  the  student,  it  matters  little  with 
which  they  are  more  particularly  associated,  while  the 
public  lecturer,  because  of  the  constant  use  of  acids  re- 
quired in  performing  the  experiments  in  Galvanism  and 
Electro-Magnetism,  will  find  it  much  the  most  convenient 
to  discuss  these  subjects,  at  least,  in  connection  with  his 
course  of  lectures  on  Chemistry.  And  if  we  were  conv 


PREFACE.  V 

pelled  to  draw  a  line  between  these  two  branches  of 
science,  so  as  to  make  each  as  independent  of  the  other  as 
possible,  we  should  be  obliged  to  make  the  same  division; 
since  a  course  of  study  in  Natural  Philosophy  will  be 
quite  complete,  as  far  as  it  goes,  without  including  the 
doctrines  of  Heat  or  Galvanism,  both  of  which,  however, 
lie  at  the  very  foundation  of  a  Chemical  course,  and  can- 
not be  dispensed  with  from  the  most  elementary  treatise 
on  the  subject.  It  is  believed,  therefore,  that  the  divi- 
sion adopted  is  not  only  theoretically  correct,  but  that 
it  will  be  found,  in  practice,  more  convenient  than  any 
other  to  the  teacher,  and  more  advantageous  to  the 
student. 

In  the  articles  on  Electricity  and  Magnetism,  and 
perhaps  in  a  few  other  instances,  persons  making  use 
of  both  works  will  observe  a  little  repetition,  but  not  so 
much  as  to  occasion  any  inconvenience. 

The  following  is  a  list  of  the  works  chiefly  made  use 
of  in  compiling  the  present  volume,  viz:  —  Elements  of 
Natural  Philosophy,  by  Dr.  Golding  Bird;  the  Trea- 
tises on  Mechanics,  Hydrostatics,  Pneumatics,  Optics, 
Optical  Instruments,  Polarization  of  Light,  Electricity 
and  Magnetism,  in  the  Library  of  Useful  Knowledge; 
the  Treatises  on  Mechanics,  Hydrostatics,  Pneumatics, 
Sound,  <fcc.,  in  the  Encyclopedia  Metropolitana ;  Cours 
de  Physique  de  1'  Ecole  Poly  technique,  par  G.  Lame* ;  a 
Treatise  on  Hydrostatics  and  Pneumatics,  by  Dr.  Lard- 
ner ;  a  Treatise  on  Optics,  by  Sir  David  Brewster ;  a 
1» 

I 


Treatise  on  Mechanics,  by  Capt.  Henry  Kater  and  Dr. 
Lardner ;  The  Philosophy  of  Sound  and  Musical  Com- 
position, by  W.  Mullinger  Higgins ;  a  Manual  of  Elec- 
tricity, Magnetism  and  Meteorology,  by  Lardner  and 
Walker ;  Experimental  Researches  in  Electricity,  by 
Sir  M.  Faraday ;  and  Scientific  Dialogues,  by  Rev.  J. 
Joyce.  Besides  these,  occasional  reference  has  been 
made  to  a  few  other  works,  as  the  Encyclopedias,  Sci- 
entific Journals,  &c. 

The  writer  would  not  omit  the  occasion  to  tender  his 
acknowledgments  to  those  of  his  friends  who  have  fa- 
voured him  by  their  counsel  during  the  preparation  of 
the  work,  and  to  express  the  hope  that  it  may  not  be 
found  unworthy  of  the  interest  they  have  manifested  in 
its  progress. 

Middktown,  Ct.9  Oct.  1,  1845. 


CONTENTS. 


CHAPTER   I. 

MECHANICS Page  11 

FIRST  PRINCIPLES 11 

Cohesion 15 

Capillary  Attraction 16 

GRAVITATION 22 

Centre  of  Gravity 26 

MOTION  AND  FORCE 32 

Curvilinear  Motion • 37 

LAW  OP  FALLING  BODIES 39 

COLLISION  OP  BODIES 49 

THE  PENDULUM 53 

MECHANICAL  POWERS 56 

The  Lever 57 

The  Wheel  and  Axle 61 

The  Pulley 64 

The  Inclined  Plane 68 

The  Wedge 69 

The  Screw 69 

Friction 72 

CHAPTER  II. 

HYDROSTATICS 73 

Pressure  applied  to  Liquids 76 

Pressure  produced  by  the  Weight  of  Liquids 79 

(7) 


Vlll  CONTENTS. 

Immersion  of  Solids  in  Liquids 88 

Specific  Gravity 95 

Motion  of  Liquids 100 

Hydraulic  Machines 105 

CHAPTER    III. 

PNEUMATICS 108 

THE  AIR  PUMP 110 

PRESSURE  AND  ELASTICITY  OF  THE  AIR 113 

The  Barometer , .  116 

Other  Instances  of  Atmospheric  Pressure 120 

Elasticity  and  Compressibility  of  Air 122 

MACHINES  FOR  RAISING  WATER  —  PUMPS 127 

Suction  Pump 127 

Forcing  Pump 128 

The  Fire  Engine 129 

The  Lifting  Pump 130 

Hiero's  Fountain 131 

Bellows 132 

The  Syphon 133 

Intermittent  Springs 135 

The  Diving  Bell 136 

Weight  of  Bodies  in  Air 138 

Balloons 139 

The  Steam  Engine 142 

Rotary  Steam  Engine 147 

Meteorology 147 

CHAPTER   IV. 

ACOUSTICS . . 154 

Music 160 

Vibrations  of  Bodies. .  .166 


CONTENTS.  IX 

The  Ear 167 

The  Voice 168 

Ventriloquism 169 

CHAPTER   V. 

OPTICS 169 

REFLECTION  OF  LIGHT 174 

Formation  of  Images  by  Reflection 177 

REFRACTION  OF  LIGHT 183 

Total  Reflection  of  Light 186 

Progress  of  Light  through  different  Media 186 

Formation  of  Images  by  Lenses 190 

SEPARATION   OF  THE   DIFFERENT  COLOURED   RAYS. — 

COLOURS  OF  BODIES 193 

Fixed  Lines  of  the  Spectrum 198 

Illuminating  Power  of  the  Spectrum 199 

Colours  of  Bodies 199 

The  Rainbow 201 

POLARIZATION  OF  LIGHT.  —  DOUBLE  REFRACTION 209 

Polarization  of  Light  by  Reflection 209 

Polarization  of  Light  by  Double  Refraction 213 

Polarization  of  Light  by  Absorption 216 

Polarization  of  Light  by  Successive  Reflections 217 

Colours  produced  by  Polarization 218 

CHAPTER    VI. 

VISION 223 

Structure  of  the  Eye  —  Use  of  Spectacles 231 

OPTICAL  INSTRUMENTS 239 

Photometers ' 239 

The  Kaleidoscope 240 

The  Camera  Obscura  .  ,  . . . .  .  240 


X  CONTENTS. 

The  Camera  Lucida 244 

The  Magic  Lantern 244 

The  Solar  Microscope 245 

The  Single  Microscope 245 

The  Multiplying-Glass 247 

The  Compound  Microscope 248 

Telescopes 250 

CHAPTER   VII. 

MAGNETISM 256 

The  Magnetic  Needle 258 

Terrestrial  Magnetism 265 

The  Dipping-Needle 266 

Theories  of  Magnetism 270 

CHAPTER   VIII. 

ELECTRICITY 271 

The  Electrical  Machine 277 

Various  Experiments 278 

INDUCTION 284 

The  Electrophorus 286 

Electrometers 287 

The  Leyden  Jar 288 

The  Universal  Discharger 290 

The  Condenser 292 

ATMOSPHERIC  ELECTRICITY 293 

Lightning-Rods 297 

Water-Spouts  and  Land-Spouts 298 

The  Aurora  Borealis  . .  .300 


NATURAL  PHILOSOPHY. 


C  H  A  P  T  E  R  J«  . 

MECHANICS. 


1.  First  Principles.  —  Matter  is  the  general  name  for  every- 
thing or  substance  that  has  length,  breadth  and  thickness,  and 
which  is  capable  of  affecting  the  senses. 

2.  It  is  the  object  of  Natural  Philosophy  to  make  us  acquaint- 
ed with  the  various  qualities  or  properties  of  matter,  and  the 
manner  in  which  different  masses  of  it  affect  each  other. 

3.  There  are  certain  general  properties  which  are  common 
to  all  kinds  of  matter,  as  magnitude,  figure  or  form,  impenetra- 
bility, inertness,  divisibility,  attraction,  &c.     But  before  pro- 
ceeding to  the  discussion  of  these,  several  mathematical  terms, 
that  will  sometimes  occur,  must  be  explained. 

4.  A  point  is  supposed  to  be  without  length,  breadth,  or  thick- 
ness ;  a  mere  division  between  two  lines. 

A  line  is  mere  length  without  breadth  or  thickness ;  it  is  in- 
deed a  mere  division  between  two  surfaces,  as  two  pieces  of 
paper,  the  edges  of  which  we  may  suppose  in  contact. 

A  surface  is  supposed  to  have  length  and  breadth  without 
thickness,  and  may  be  considered  as  dividing  two  solids  which 
are  in  contact. 

A  plane  is  a  surface  on  which,  if  a  straight  line  be  placed,  it 
will  touch  at  every  point. 

A  solid  is  a  body  having  length,  breadth,  and  thickness. 
An  angle  is  the  opening  made  by  two  straight  lines  which 
meet  at  some  point. 

B  Thus,  the  opening  A,  figure  1,  made 

~^— -^^_^  by  the  two  lines  BC  and  C  D,  is  called 

o the  angle  A,  or  the  angle  BCD,  which 
means  the  same. 

rig,  i.          

Question  1.  What  is  matter  ?  2.  What  is  the  object  of  Natural  Philoso- 
phy ?  3.  What  are  some  of  the  general  properties  of  matter  ?  4.  What  is 
a  point  ?  A  line  ?  A  surface  ?  A  solid  ?  An  angle  ?  A  right  angle  ?  An 
acute  angle  ?  An  obtuse  angle  ?  How  are  angles  measured  ? 

(11) 


12 


NATURAL     PHILOSOPHY 


When  one  of  the  lines  meets  the  othei 
so  as  to  make  equal  angles  on  each  side 
of  it,  those  angles  are  said  to  be  right  an- 
gles. The  angles  ABC  and  A  B  D,  figure 
2,  are  right  angles. 


Fig.  2. 


An  angle  greater  than  a  right  angle,  as  A  B  C, 
figure  3,  is  called  an  obtuse  angle;  one  less  than 
a  right  angle,  as  the  angle  BC  D,  figure  1,  is  call- 
ed an  acute  angle. 


Fig.  4. 


Fig.  3. 

The  magnitude  of  an  angle  is  usually 
estimated  by  the  part  of  the  circumfer- 
ence of  a  circle  included  between  its 
sides,  supposing  the  point  of  meeting  of 
the  two  lines  to  be  at  the  centre.  The 
E  whole  circumference  for  this  purpose  is 
supposed  to  be  divided  into  360  parts, 
called  degrees.  Therefore  A  C  B,  figure 
4,  is  an  angle  of  45  degrees  (usually 
written  45°),  and  A  C  D  an  angle  of  90°. 
So  B  C  E  is  an  angle  of  135°. 

5.  Upon  examining  the  various  properties  of  bodies,  we  ob- 
serve, that  several  of  them  are  essential  to  and  inseparable  from 
every  form  of  matter.     Such  are  magnitude,  form  or  figure, 
and  impenetrability.  We  cannot  even  conceive  of  a  particle  of 
matter  existing  without  these.    They  are  therefore  called  the 
essential  properties  of  matter. 

6.  Other  properties  are  considered  as  secondary  or  incidental, 
as  attraction,  colour,  divisibility,  inertness,  hardness,  elasticity, 
flexibility,  &c. 

7.  By  the  magnitude  or  extension  of  a  body,  we  mean  its 
length,  breadth  and  thickness,  or  its  power  of  occupying  a  cer- 
tain portion  of  space,  without  which  we   of  course  cannot 
conceive  it  to  exist.     And  as  the  space  occupied  by  a  body 
must  be  limited,  every  body  or  portion  of  matter  must  possess 
some  form  or  figure,  which  is  only  the  limits  of  extension. 


Quest.  5,  6.  What  incidental  properties  of  matter  are  mentioned  ? 
What  is  meant  by  the  magnitude  of  a  body  ? 


7. 


MECH  AN  ICS.  13 

8.  By  the  impenetrability  of  matter,  we  mean  that  one  por- 
tion of  it  will  not  permit  another  portion  to  occupy  the  same 
space  at  the  same  time.     There  are  three  kinds  or  forms  of 
matter,  as  we  shall  see  more  fully  hereafter;  viz.,  solids,  as 
gold,  iron,  wood,  &c. ;  liquids,  as  water,  oil,  mercury,  &c. ;  and 
the  gases,  as  the  air,  which  constantly  surrounds  us,  carbonic 
acid,  &c. 

Now  solids,  we  know  by  daily  observation,  will  not  allow 
other  bodies  to  occupy  the  same  space  with  themselves,  at  the 
same  time;  and  the  same  may  be  shown  of  liquids  and  gases. 
When  a  stone  or  other  heavy  solid  is  thrown  into  water,  it 
sinks  into  it,  but  it  first  pushes  away  or  removes  the  water  in 
order  to  make  room  for  itsel£  So,  if  we  turn  a  glass  tumbler 
bottom  upward,  and  press  it  down  perpendicularly  into  a  vessel 
of  water,  the  water  does  not  rise  and  fill  it,  because  of  the  air 
it  contains.  It  does  indeed  rise  a  little  in  the  tumbler,  because 
the  air  is  compressed  together,  but  no  force  can  make  the  water 
fill  the  glass  entirely,  unless  the  air  is  first  allowed  to  escape. 

9.  By  the  inertness  of  matter  is  meant  its  inability  to  put 
itself  in  motion,  or  to  stop  itself  when  once  put  in  motion.     It 
is  sometimes  called  inertia,  and  is  simply  resistance  to  a  change 
of  state,  whether  of  rest  or  motion.     Thus  a  body,  as  a  cannon 
ball,  being  once  at  rest,  would  forever  remain  so  unless  acted 
on  by  some  external  force ;  so  when  once  put  in  motion,  as 
when  it  is  fired  from  the  cannon,  were  it  not  for  the  resistance 
it  meets  with  from  the  atmosphere  and  other  causes,  it  would 
continue  to  move  forever  with  the  same  uniform  velocity. 

This  of  course  cannot  be  demonstrated,  though  it  is  no  doubt 
true.  A  body  put  in  motion  by  man  does  indeed  soon  come  to  a 
state  of  rest,  but  the  continuance  of  its  motion  depends  greatly 
upon  the  resistance  it  meets  with,  the  motion  continuing  longer 
in  proportion  as  the  resistance  is  less.  Thus  a  body  will  move 
longer  on  smooth  ice  than  on  a  floor,  and  longer  through  the 
air  than  on  smooth  ice.  If  all  resistance,  therefore,  could  be 
removed,  we  infer  the  motion  of  the  body  would  be  perpetual. 

10.  Every  portion  of  matter  with  which  we  are  acquainted 
is  capable  of  being  separated  or  divided  into  parts;  but  it  is 
believed  that  every  body  is  made  up  of  an  immense  number 
of  particles  or  atoms  which  are  almost  inconceivably  minute, 
and  entirely  incapable  of  destruction  or  division.    These  parti- 

Quest.  8.  What  is  meant  by  the  impenetrability  of  matter  ?  What  three 
forms  of  matter  are  there  ?  How  is  it  shown  that  water  and  air  are  impene- 
trable ?  9.  What  is  meant  by  the  inertness  of  matter  ?  What  is  the  reason 
that  a  body  once  put  in  motion  does  not  continue  to  move  forever  ?  10.  Is 
every  portion  of  matter  capable  of  being  separated  or  divided  into  parts  ?  Are 
their  ultimate  particles  or  atoms  incapable  of  division  ?  Can  these  particles 
be  made  visible  to  the  eye  ?  What  is  said  of  the  divisibility  of  gold  ?  Into 
how  long  a  thread  has  a  pound  of  wool  been  spun  ?  In  what  bodies  do  we 
have  the  most  extreme  division  of  matter  ? 
2 


14  NATURAL     PHILOSOPHY. 

cles  are  so  very  small,  that  no  glass,  however  great  its  magni- 
fying power,  has  yet  been  able  to  show  them,  nor  is  anything 
really  known  of  their  form  or  dimensions;  but  yet  it  is  believed 
there  is  sufficient  proof  of  their  existence. 

But  matter,  though  composed  of  minute,  unchangeable  par- 
ticles, is  divisible  to  a  surprising  extent.  An  ounce  of  gold  can 
be  drawn  into  a  wire  several  miles  in  length,  and  yet  no  flaw  or 
evidence  of  separation  between  its  atoms  can  by  any  means 
be  discovered.  So  gold  leaf  may  be  beaten  out  with  the  ham- 
mer so  thin  that  360,000  of  them  will  be  required  to  equal  an 
inch  in  thickness ;  and  in  the  form  of  gilding  for  silver- wire  it 
is  often  much  thinner  even  than  this.  An  exceedingly  small 
portion  of  the  substance  called  strychnia  will  diffuse  itself 
through  a  whole  pint  of  water,  and  render  every  drop  bitter ; 
and  a  single  grain  of  hyposulphite  of  silver  mixed  with  a  little 
aqua  ammonij^will  sweeten  32,000  grains  of  water.  A  few 
years  ago  a  .jpqKian  in  England  spun  a  single  pound  of  wool 
into  a  threaa  168?300  yards,  or  nearly  100  miles  in  length. 

But  it  is  in  the  case  of  odoriferous  bodies  probably  that  we 
have  the  most  extreme  division  of  matter.  A  small  piece  of 
musk  or  camphor  will  fill  a  room  with  its  particles,  which  are 
constantly  thrown  off  and  float  in  the  atmosphere,  for  a  great 
length  of  time  without  losing  but  a  small  part  of  its  weight. 

11.  There  are  animalcules  so  small  that  a  single  drop  of 
water  may  contain  more  than  26,000  of  them ;  and  150,000,000 
would  have  ample  room  in  a  tumbler  of  water  to  perform  all 
their  evolutions  without  interfering  with  each  other.    It  is  to 
be  remembered  too  that  each  of  these  minute  beings  must  have 
its  various  organs  of  circulation,  respiration,  locomotion,  &c. 
How  inconceivably  small  then  must  be  the  particles  of  which 
their  bodies  are  composed ! 

12.  The  particles  of  which  all  bodies  are  composed  possess 
another  property  called  attraction,  which  causes  them  to  adhere 
together  with  greater  or  less  force.     This  is  called  the  attrac- 
tion of  cohesion.     We  know  nothing  of  its  cause,  but  give  the 
name  to  the  force  by  which  the  particles  of  bodies  are  held  to- 
gether. 

13.  There  are  also  other  varieties  of  attraction,  as  the  attrac- 
tion of  gravitation,  capillary  attraction,  electrical  attraction, 
magnetic  attraction,  and  chemical  attraction  or  affinity.    Elec- 
trical and  magnetic  attraction  will  be  treated  of  under  electri- 
city and  magnetism  respectively,  but  the  discussion  of  affinity 
belongs  exclusively  to  chemistry. 

Quest.  11.  How  many  animalcules  may  be  contained  in  a  single  drop  of 
water  ?  Must  each  of  these  have  the  different  organs  of  respiration,  circula- 
tion, &c.  ?  12.  What  is  meant  by  attraction  ?  13.  What  varieties  of  attrac^ 
tion  are  mentioned? 


MECHANICS. 


15 


14.  Cohesion.  —  All  bodies  being  composed  of  particles  of 
incalculable  minuteness  which  are  capable  of  being  separated 
from  each  other,  it  follows  that  there  must  be  some  force  by 
virtue  of  which  solid  bodies  maintain  their  form,  and  their  parts 
are  preserved  from  being  scattered  like  those  of  fluids  merely 
by  their  own  weight.  This  force  is  called  cohesion,  or  some- 
times the  attraction  of  cohesion.  It  is  the  force  by  which  the 
parts  of  all  bodies  are  prevented  from  separating  from  each 
other,  and  falling  to  pieces ;  and  when  a  body  is  broken  it  is 
this  force  which  is  overcome.  It  is  exerted  only  when  the 
particles  are  apparently  in  contact,  or  the  distance  between 
them  is  insensible.  Thus,  if  two  drops  of  mercury  are  brought 
near  each  other  on  a  plate  of  glass,  they  remain  separate  until 
they  approach  so  near  each  other  that  they  appear  to  touch, 
when  they  immediately  unite  and  form  a  single  globule. 

If  a  plate  of  metal  or  glass 
be  suspended  in  a  balance, 
and  exactly  counterpoised 
by  weights,  as  in  figure  5, 
a  slight  additional  weight 
at  A  will  cause  the  plate  C 
to  rise;  but  if  now  a  basin 
of  water  B  is  put  under  it, 
so  that  it  shaH  just  touch 
the  surface  of  the  water,  it 
will  be  found  that  a  consi- 
derable additional  weight 
will  be  required  at  the  op- 
Fig.  5.  posite  end  of  the  beam  to 
detach  the  plate  from  the  fluid  surface,  in  consequence  of  its 
cohesive  attraction.  So  two  plates  of  glass  finely  polished  and 
a  little  moistened,  when  pressed  firmly  together,  adhere  with 
considerable  force.  If  two  lead  bullets  are  each  scraped  clean 
on  one  side  and  pressed  together,  one  of  them  being  turned  or 
twisted  a  little  at  the  same  time,  they  may  be  made  to  unite  so 
firmly  that  it  will  require  a  force  equal  to  a  number  of  pounds 
to  separate  them.  Two  freshly  cut  surfaces  of  caoutchouc  or 
India  rubber,  when  firmly  pressed  or  hammered  together,  if 
perfectly  dry  and  warm,  will  cohere  almost  as  firmly  as  if  they 
originally  formed  but  one  piece. 

In  liquids  this  force  is  feeble,  though,  as  we  have  seen,  it  is 
not  wanting.  It  is  this  which  causes  the  drop  of  water  to  ad- 

Quest.  14.  What  is  cohesion  ?  What  force  is  overcome  when  a  body  is 
broken?  At  what  distance  only  is  it  exerted  ?  How  is  this  shown  by  two 
drops  of  mercury  on  a  plate  ?  How  is  it  shown  by  a  metallic  plate  suspended 
from  a  balance  on  the  surface  of  water  ?  Will  two  plates  of  polished  glass 
adhere  with  considerable  force  ?  How  may  two  lead  balls  be  made  to  ad- 
here ?  Is  there  any  cohesion  among  the  particles  of  liquids  ?  How  is  the 
presence  of  cohesion  in  liquids  shown  ? 


16  NATURAL     PHILOSOPHY. 

here  to  the  lip  of  the  vessel  from  which  it  is  poured,  and  to 
trickle  down  the  side  instead  of  dropping1  perpendicularly 
downwards,  as  would  be  the  case  if  no  attraction  existed  be- 
tween the  solid  of  which  the  vessel  is  composed  and  the  liquid, 
It  is  this  force,  indeed,  which  causes  water  to  wet  any  other 
substance,  as  this  effect  could  not  be  produced  but  for  its 
existence. 

15.  Sometimes,  when  the  bodies  that  adhere  are  of  different 
kinds,  as  in  the  case  of  the  metallic  plate  and  the  water  above 
described,  or  in  the  case  of  the  silvering  upon  the  back  of  a 
looking-glass,  the  term  adhesion  is  used,  leaving  the  term  cohe- 
sion to  be  applied  only  to  those  instances  in  which  the  particles 
are  of  the  same  kind  ;  but  the  distinction  is  unimportant. 

16.  Capillary  Attraction.  —  That  force  by  which  water  or 
other  liquids  are  made  to  rise  in  very  small  tubes  is  called 
capillary  attraction.    The  effect  of  the  same  force  is  also  seen 
whenever  a  plate  or  rod  of  any  substance  is  plunged  into  a 
fluid  capable  of  moistening  it,  as  a  plate  of  glass  in  water,  by 
the  rise  of  a  small  portion  of  the  water  against  its  sides,  as  if 
attracted  by  the  glass. 

Thus,  let  AB,  figure  6,  be  the 
level  surface  of  the  water  in  a  basin, 
C  a  section  of  the  glass  plate,  one 
B  edge  of  which  is  plunged  vertically 
into  the  water.  The  water,  as  every 
one  has  observed,  will  rise  a  little 
above  the  level  surface,  against  the 
sides  of  the  glass  plate,  as  repre- 
sented  by  the  dotted  curved  lines 
in  the  figure.  The  same  effect  is  also  seen  in  the  similar  rise 
of  the  water  around  the  sides  of  a  tumbler  or  other  vessel  con- 
taining it,  and  indeed  in  most  liquids,  when  contained  in  vessels 
in  ordinary  use.  In  order  that  it  may  take  place,  it  is  only 
necessary  that  the  liquid  should  be  of  such  a  nature  as  to  be 
capable  of  moistening  the  substance  of  which  the  vessel  is 
formed. 

But  these  phenomena  are  best  observed  by  using  small  glass 
tubes,  and  water  coloured  with  ink,  or  other  colouring  matter. 
The  smaller  the  bore  of  the  tube  is,  the  higher  the  water  will 
rise. 

Quest.  15.  When  has  the  term  adhesion  been  used  ?  16.  What  is  capiN 
lary  attraction  ?  How  is  it  shown  when  a  plate  or  rod  is  plunged  into  a  liquid  ? 
Does  the  water  always  rise  a  little  around  the  sides  of  vessels  in  which  it  is 
contained  ?  In  order  that  this  rise  may  take  place,  what  only  is  necessary  ? 
How  are  the  phenomena  of  capillary  attraction  best  observed  ?  On  what 
does  the  height  to  which  the  liquid  will  rise  depend  ?  Will  a  liquid  always 
rise  to  the  same  height  in  tubes  of  the  same  bore  ?  Will  all  liquids  rise  to 


MECHANICS.  17 

This  is  shown  in  figure  7,  in  which 
A  B  C  D  represent  several  tubes  of  dif- 
ferent bore,  open  at  both  ends,  and  im- 
mersed in  water,  and  II II,  the  heights  to 
which  the  water  rises  in  them  severally. 
It  attains  the  greatest  height  in  small  hair- 
like  tubes;  and  hence  the  force  which 
F'g-  7.  causes  the  rise  is  called  capillarity,  or  capil- 

lary attraction,  from  the  Latin  word  capittus,  a  hair. 

The  height  to  which  water  will  rise  in  tubes  of  the  same  bore 
is  always  the  same ;  but  of  other  liquids,  as  oil  of  vitriol,  alcohol, 
or  solution  of  common  salt,  some  will  rise  higher,  and  others 
not  so  high.  When  the  bore  of  the  tube  is  one-eighth  of  an 
inch,  water  will  rise  about  a  quarter  of  an  inch. 

This  force  is  also  exerted  between  two  plates,  when  brought 
sufficiently  near  each  other,  and  immersed  in  a  fluid. 

The  experiment  is  best  performed 
by  taking  two  pieces  of  glass,  A  and 
B,  figure  8,  an  inch  and  a  half  wide, 
and  two  inches  long,  and  placing  them 
in  a  trough  of  coloured  water,  D,  with 
two  of  the  edges  in  contact  as  at  C, 
while  the  opposite  edges  are  a  little 
- s.  separated.  The  two  plates  will  then 

make  a  small  angle  with  each  other,  and  the  water  will  be  ob- 
served to  rise  to  a  considerable  height  on  the  side  C,  where  the 
plates  touch  each  other,  and  gradually  to  fall  towards  the 
other  side,  forming  the  well-known  curve  called  the  hyper- 
bola. 

If  a  drop  of  water  is  placed  in  a  small  conical  tube,  by  the 
force  of  capillarity  it  immediately  begins  to  move  towards  the 
smallest  end  of  the  tube,  whatever  may  be  its  position. 

It  is  by  this  force  of  capillarity  that  water  rises  in  a  piece  of 
sponge,  or  cloth,  or  other  similar  substance,  as  oil  in  the  wicks 
of  lamps,  &c.,  which  may  be  considered  as  a  collection  of  a 
great  many  short  capillary  tubes,  promiscuously  thrown  toge- 
ther. By  the  same  force  water  is  raised  from  the  depth  of 
several  feet  beneath  the  surface  of  the  earth  to  keep  the  soil 
moist,  from  which  it  is  constantly  evaporating  by  the  heat  of 
the  sun.  Were  it  not  for  this  provision  of  nature,  the  surface 
of  the  earth  would  often  become  so  thoroughly  dry  and  parch- 
ed, during  the  long  intervals  that  occur  without  rain,  that  all 
vegetation  must  necessarily  be  destroyed.  But  the  water  which 

the  same  height  ?  Will  this  force  be  exerted  between  two  plates  ?  What 
is  the  effect  when  a  drop  of  water  is  placed  in  a  conical  tube  ?  How  is  the 
rise  of  water  in  a  sponge  or  piece  of  cloth  explained  ?  How  may  such  porous 
substances  be  considered  ?  How  may  we  account  for  the  rise  of  the  water 
in  the  soil  from  the  depth  of  several  feet  ?  Is  this  an  important  provision  of 
2* 


18  NATURAL     PHILOSOPHY. 

accumulates  beneath  the  surface  during  rains,  is  preserved 
there  as  in  a  reservoir,  and  gradually  rises  by  capi  larity  as  it 
is  needed  to  supply  the  constant  wants  of  vegetation. 

To  illustrate  this  point,  take  a  piece  of  glass  tube,  open  at 
both  ends,  and  not  less  than  half  an  inch  in  diameter,  and  from 
twelve  to  eighteen  inches  long,  and  support  it  as  nearly  as  may 
be  in  a  perpendicular  position,  in  a  shallow  vessel  capable  of 
holding  water.  Then,  after  stopping  the  lower  end  loosely,  rill 
the  tube  with  perfectly  dry  sand  or  loam,  and  pour  into  the 
basin  some  water ;  it  will  be  seen  that  the  water  will  gradually 
rise  in  the  tube,  moistening  the  sand  until  it  reaches  quite  to 
the  top,  though  if  the  tube  is  eighteen  or  twenty  inches  long, 
it  may  require  several  days  for  the  purpose. 

Capillary  attraction  is  in  some  instances  made  to  exert  great 
force.  A  weight  suspended  by  a  rope  perfectly  dry  will  be 
drawn  up  a  considerable  height,  if  the  rope  is  moistened  with 
water.  The  fibres  of  the  rope  pass  spirally  around  it,  and  their 
swelling  by  absorbing  the  water,  which  is  due  to  capillary  at- 
traction, necessarily  occasions  a  contraction  in  its  length.  If 
the  rope  is  sufficiently  strong,  it  may  be  made  in  this  way  to 
lift  several  hundred  pounds. 

17.  When  a  solid  is  immersed  in  a  liquid  which  will  not  ad- 
here to  it  so  as  to  moisten  it,  then,  instead  of  an  elevation  of  the 
liquid,  we  see  a  depression.  This  is  the  case  with  mercury  in  a 
glass  vessel,  all  around  the  sides  of  which  a  depression  will 
always  be  observed.  When,  therefore,  a  capillary  glass  tube 
is  plunged  into  a  vessel  of  mercury,  the  fluid  metal  will  not  rise 
so  high  in  it  as  the  surface  of  that  contained  in  the  vessel. 

It  is  on  this  principle  that  a  small  sewing-needle  may  some- 
times be  made  to  float  upon  the  surface  of  water.  To  insure 
success  in  the  experiment,  the  needle  should  first  be  oiled 
slightly  and  wiped  clean,  and  then  placed  very  carefully  upon 
the  surface  of  the  water.  The  perspiration  of  the  hand  is  of 
sufficiently  oily  a  nature  to  prevent  the  water  from  adhering  to 
the  needle ;  or  it  may  be  rubbed  upon  the  hair,  and  then  wiped 
clean.  If  the  surface  of  the  needle  is  once  moistened,  it  imme- 
diately sinks. 

Some  insects  are  enabled  to  walk  upon  the  surface  of  water 
by  means  of  this  repulsion  between  their  feet  and  legs  and  the 
water.  The  same  repulsion  is  seen  in  drops  or  even  large 
globules  of  dew  that  are  often  observed  standing  upon  the 
leaves  of  plants,  particularly  the  cabbage.  When  the  leaf  is 

nature  ?  How  may  the  rise  of  water  in  the  soil  be  illustrated  by  means  of  a 
tube  filled  with  sand  ?  Is  capillary  attraction  exerted  with  any  considerable 
force  ? 

Quest.  17.  What  is  the  effect  when  a  solid  is  immersed  in  a  liquid  which 
is  not  capable  of  moistening  it  ?  How  may  a  small  sewing-needle  be  made 
to  float  upon  water  ?  How  are  some  insects  able  to  walk  upon  the  surface 
of  water  ?  Why  does  a  drop  of  water  roll  unbroken  upon  a  cabbage-leaf  ? 


MECHANICS.  19 

moved,  the  water  will  often  roll  off  quite  unbroken,  leaving  the 
leaf  of  the  plant  dry. 

18.  A  slight  modification  of  the  action  of  this  same  force  is 
seen  in  the  attractions  and  repulsions  which  take  place  between 
two  balls,  or  other  light  substances,  when  thrown  upon  the 
surface  of  water  or  other  liquids.     When  two  balls,  both  of 
which  are  capable,  or  both  incapable  of  being  wet  with  water, 
are  made  to  float  upon  the  surface  of  this  liquid,  if  they  come 
within  a  certain  distance  of  each  other,  they  are  observed  to 
rush  together,  as  though  an  attraction  existed  between  them. 
Balls  of  wax  or  wood  will  answer  for  the  purpose. 

A  and  B,  figure  9,  are  supposed  to  be 
two  balls  of  the  former  substance  float- 
ing upon  water.  As  the  water  will  not 

readily  moisten  the  wax,  a  cavity  is 

Fig  9  produced  around  the  balls;  and  if  they 

come  within  a  certain  distance  of  each 
other,  the  surface  of  the  water  at  C  will  be  depressed  a  little 
below  the  general  level,  and  the  pressure  against  the  outside 
of  each  will  then  be  greater  than  that  against  the  inside.  As  a 
necessary  consequence,  they  will  rush  together. 

If  both  balls  are  capable  of  being  moistened  with  the  liquid, 
then  the  surface  at  C  between  them  will  tend  to  rise  a  little 
above  the  general  level,  and  will  thus  draw  the  balls  together. 
But  if  one  of  the  two  balls  used  is  of  such  a  nature  that  its  sur- 
face may  be  moistened  by  the  liquid  used,  while  that  of  the 
other  ball  is  incapable  of  it,  then  they  will  appear  to  repel  each 
other. 

The  balls  D  and  E,  figure  10,  are 
supposed  to  be  of  this  character.     One 
of  the  balls,  D,  raises  the  water  all 
around  it  by  the  attraction  of  its  sur- 
F.  r  10  face,  while  the  other  repels  it ;  so  that, 

when  brought  together,  the  latter  seems 
to  slide  off  from  the  heap  of  water  raised  by  the  former. 

The  same  attractions  and  repulsions  are  observed  between 
the  sides  of  a  vessel  containing  a  liquid,  and  substances  floating 
in  it. 

19.  Closely  allied  with  capillarity  are  the  phenomena  of  en- 
dosmose  and  exosmost>.   When  two  liquids  of  different  densities 
are  separated  by  a  membrane,  as  a  piece  of  bladder,  or  unoiled 

Quest.  18.  When  will  two  balls  thrown  upon  the  surface  of  water  appear 
to  attract  each  other  ?  What  substances  may  be  used  for  the  purpose  ? 
What  will  be  the  effect  if  one  of  the  balls  is  moistened  by  the  liquid  used 
and  the  other  is  not  ?  19.  What  is  the  effect  when  two  liquids  of  different 
densities  are  separated  by  a  thin  membrane,  as  a  piece  of  moistened  leather, 
or  by  a  porous  substance  ?  In  what  direction  does  the  liquid  move  through 
the  membrane  ?  What  other  properties  are  closely  connected  with  cohe- 
sion 1 


20  NATURAL     PHILOSOPHY. 

leather,  or  by  unglazed  porcelain,  two  currents  become  estab- 
lished, one  from  within  to  without  (exosmose),  the  other  in  the 
contrary  direction  (endosmose). 

A  good  method  to  illustrate  it  is  to  take  a  glass 
tube  half  an  inch  or  more  in  diameter,  as  B,  figure  1 1, 
and  tying  a  piece  of  bladder  or  unoiled  leather  over 
one  end  for  a  bottom,  as  seen  in  the  figure  at  A,  put 
in  some  sugar  and  stand  it  in  a  tumbler  of  water,  C, 
at  the  same  time  pouring  a  little  water  into  the  tube 
upon  the  sugar.  In  the  course  of  a  few  hours  the 
water  will  be  found  to  rise  in  the  tube,  having  entered 
by  endosmose  through  the  leather  at -the  bottom  of 
the  tube.  If  the  tube  is  allowed  to  stand,  the  liquid 
will  rise  after  a  number  of  days  to  the  height  of  se- 


Fig.  11.  veral  feet.  If  the  sugar  had  been  put  into  the  tumbler 
outside  of  the  tube,  and  pure  water  in  the  tube,  exosmose 
would  have  taken  place,  and  the  tube  have  become  empty.  As 
a  general  rule,  it  is  found  that  the  least  dense  liquid  has  a  ten- 
dency to  pass  to  the  most  dense,  and  of  course  to  dilute  it. 
This  is  the  case  in  the  above  instance,  the  solution  of  sugar 
being  of  course  more  dense  than  the  water. 

Closely  connected  with  cohesion  are  several  other  properties 
which  seem  to  be  accidental,  as  tenacity,  brittleness,  elasticity, 
and  flexibility. 

20.  The  tenacity  of  bodies  is  dependent  directly  upon  the  in- 
tensity of  the  attractive  force  among  the  particles,  by  which 
they  are  prevented  from  being  separated  so  far  as  to  cause  a 
rupture  or  fracture  of  the  mass.     This  property  varies  greatly 
in  different  substances,  the  metals  being  in  general  most  tena- 
cious.   But  in  the  metals  there  is  a  great  difference,  a  force  of 
about  twenty  pounds  being  sufficient  to  draw  asunder  a  wire 
of  bismuth  y^th  of  an  inch  in.  diameter,  while  an  iron  wire  of 
the  same  size  would  support  a  weight  of  more  than  five  hun- 
dred and  forty  pounds.   Next  to  iron,  copper  and  platinum  are 
most  tenacious. 

21.  Brittleness  is  obviously  the  reverse  of  tenacity;  bodies 
that  are  brittle  are  capable  of  supporting  little  weight.    This 
property  is  often  associated  with  hardness,  and  is  frequently 
acquired  by  bodies  in  the  process  of  hardening.     Thus  steel, 
when  made  very  hard,  is  at  the  same  time  exceedingly  brittle  ; 
cutting  instruments  are,  therefore,  usually  made  partly  of  iron 
to  give  them  the  necessary  strength. 

22.  When  a  body  is  capable  of  being  bent  in  any  manner, 
within  moderate  limits,  by  the  application  of  force,  it  is  said  to 

Quest.  20.  On  what  is  the  tenacity  of  a  body  dependent  ?  Does  this  pro- 
perty of  bodies  vary  considerably?  What  metal  is  most  tenacious?  21. 
What  is  said  of  brittleness  ?  May  a  hard  body  be  at  the  same  time  brittle  ? 
22.  When  is  a  body  said  to  be  flexible  f  What  is  necessary  in  a  body  pos- 


MECHANICS.  t  21 

be  flexible ;  for  a  body  to  possess  this  property  it  is  necessary 
that  the  attraction  existing  between  one  portion  of  its  atoms 
should  be  capable  of  being  partially  overcome,  and  allowing 
them  to  be  separated  farther  from  each  other,  while  another 
portion  of  the  atoms  are  pressed  more  closely  together. 

Thus' Iet  AB  and  CD'  fi£ure  12» 

represent  two  rows  of  atoms  of  a 
cylindrical  rod  of  metal  or  other  sub- 
stance  capable  of  being  bent  in  the 
form  of  a  bow,  by  the  application  of 
a  sufficient  force  in  the  proper  direc- 
tion.  As  the  bending  takes  place, 
*ne  length  of  one  row  is  increased, 
wnile  that  of  the  other  is  diminished, 
as  may  be  seen  by  comparing  the 
curved  rows  EF  and  GH  with  AB 
and  C  D  respectively.  This  of  course 
can  be  accomplished  only  in  the 

manner  pointed  out  by  the  separation  of  the  atoms  of  one  row 
a  little  from  each  other,  while  those  of  the  other  row  are  press- 
ed nearer  together.  Among  the  most  flexible  bodies  are  lead, 
gold,  silver,  annealed  copper,  soft  iron,  especially  when  heated 
to  redness,  several  kinds  of  wood,  wax,  &c. 

23  By  the  elasticity  of  a  body  is  meant  its  capability  of  re- 
suming spontaneously  its  original  form  upon  the  removal  of  the 
coercive  force,  when  it  has  been  bent  as  described  above.  Elas- 
tic bodies  must  therefore  be  so  constituted  as  to  allow  a  portion 
of  their  particles  to  be  momentarily,  at  least,  removed  at  greater 
distances  from  each  other,  without  having  their  cohesion  over- 
come, and  others  of  them  pressed  into  closer  proximity  with 
each  other  without  becoming  permanently  fixed  in  that  posi- 
tion. The  attraction  between  the  partially  separated  atoms  on 
one  hand,  and  the  repulsion  between  the  unnaturally  approxi- 
mated  atoms  on  the  other,  will  both  tend  to  restore  the  body 
to  its  original  form.  Sometimes  this  change  of  form  may  be 
entirely  imperceptible  to  the  eye;  and  yet  it  is  demonstrable 
that  this  change  does  take  place.  Thus,  ivory  is  one  of  the  most 
elastic  solids  that  is  known ;  and  a  ball  of  it,  when  thrown  upon 
a  marble  floor,  rebounds  in  consequence  of  this  property,  its 
form  on  striking  the  floor  becoming  altered  and  compressed, 
but  it  exhibits  no  signs  of  it  to  the  eye. 

sessing  this  property  ?  In  what  part  of  the  body,  as  the  bending  takes  place, 
are  the  particles  pressed  nearer  together,  and  in  what  part  are  they  separated  ? 
23.  What  is  meant  by  the  elasticity  of  a  body?  How  must  an  elastic  body 
be  constituted  ?  What  will  tend  to  restore  the  body  to  its  original  form  ? 
Will  this  change  of  form  always  be  perceptible  to  the  eye  ?  How  is  this 
demonstrated  by  the  use  of  ivory  balls  ?  Do  elastic  bodies  differ  in  regard 


22  NATURAL     PHILOSOPHY. 

Different  elastic  bodies  vary  extremely  in  the  extent  to  which 
they  will  yield  without  rupture ;  but  most  solids  that  are  elastic 
suffer  more  or  less  change  of  form  by  being  long  compressed. 
The  gases,  as  atmospheric  air  and  carbonic  acid,  are  the  most 
elastic  of  all  bodies ;  they  never  yield  to  any  force,  however 
long  they  may  be  compressed. 

Among  the  most  elastic  solids  are  glass  threads,  steel  springs, 
and  unannealed  copper  and  brass. 

Liquids  are  but  slightly  elastic. 


GRAVITATION. 

24.  Cohesion  and  capillary  attraction  take  place  only  when 
the  particles  are  at  insensible  distances,  or  in  apparent  contact ; 
but  all  matter  is  endued  with  a  species  of  attraction  which  is 
exerted  at  all  distances,  and  is  constantly  in  exercise.     To  this 
force  we  give  the  name  Gravitation.    Every  one  knows  that 
when  any  substance,  as  a  stone,  is  permitted  to  fall  from  the 
hand,  it  rapidly  approaches  the  floor  in  a  straight  line.    Now 
the  stone  is  composed  of  inanimate  matter,  and  of  itself  is 
absolutely  inert,  and  incapable  of  changing  its  position  or 
state  (\  9),  consequently  its  falling  must  have  been  produced 
by  some  force  acting  upon  it.     This  force  is  found  to  be  the 
attraction  of  the  earth.     The  measure  or  amount  of  this  force 
in  the  case  of  any  particular  body  constitutes  the  weight  of  that 
body. 

25.  This  attraction  is  exerted  at  the  smallest  and  the  greatest 
distances,  between  the  smallest  masses  of  matter  and  the  earth 
on  which  they  lie  at  rest,  and  between  the  earth  and  sun  and 
other  vast  bodies  that  constitute  our  solar  system. 

26.  If  a  mass  of  lead  or  other  heavy  substance  be  suspended 
by  a  string,  it  will,  when  left  free  to  move  by  the  action  of  this 
force,  be  made  to  point  directly  to  the  earth ;  and  this  occurs 
in  every  place,  whether  in  America,  in  Europe,  or  in  India, 
proving  that  the  attraction  is  everywhere  towards  the  earth. 
By  further  examination  it  will  be  seen  also  that  the  mass  always 
tends  towards  the  centre  of  the  earth,  which  may  be  consider- 
ed the  point  from  which  the  force  emanates. 

to  the  extent  to  which  they  will  yield  without  rupture  ?     What  are  some  of 
the  most  elastic  solids  ?     Are  liquids  elastic  ? 

Quest.  24.  What  is  gravitation  ?  Is  a  stone  let  fall  from  the  hand  capable 
of  putting  itself  in  motion  ?  Why  then  does  it  move  towards  the  earth  ? 
What  is  the  weight  of  a  body  ?  25.  At  what  distances  is  gravitation  exerted  ? 
26.  To  what  point  in  the  earth  do  bodies  tend  ?  If  four  bodies  are  suspend- 
ed on  opposite  sides  of  the  earth,  what  will  be  their  position  with  reference 
to  each  other  ?  What  is  a  plumb-line  ? 


MECHANICS.  23 

This  may  be  illustrated  by  re- 
ferring to  figure  13,  in  which  the 
circle  E  is  supposed  to  represent 
a  section  of  the  earth  through  the 
centre,  and  A  B  C  D  the  position 
of  the  heavy  body  suspended 
by  a  string  in  four  different 
places  diametrically  opposite 
each  other. 

27.  From  this  it  will  be  seen 
that  two  plumb-lines,  which  are 
merely  lines  swinging  freely 
with  heavy  weights  attached  to 
them,  used  by  mechanics,  can 
never  be  perfectly  parallel  with 
each  other;  and  the  farther 
they  are  from  each  other,  the  farther  will  they  be  from  a  paral- 
lelism. 

Let  the  circle  SPUN,  figure  14,  be  a 
section  of  the  earth  from  north  to  south 
through  the  city  of  Philadelphia  (Pa.) ; 
it  will  also  pass  very  nearly  through 
Utica  in  the  State  of  New  York,  which 
is  about  three  degrees  and  eight  minutes 
north  of  the  former  place.  Now  suppose 
A  and  B  are  two  plumb-lines,  the  former 
at  Philadelphia,  and  the  latter  at  Utica ; 
they  will  tend  to  meet  at  the  centre  C, 
and  of  course  must  make  the  above  an- 
gle of  three  degrees  eight  minutes  with 
each  other.  But  in  the  ordinary  practice 
of  the  mechanic,  as  in  carpentry,  the 
error  that  would  be  occasioned  by  con- 
sidering such  lines  parallel,  may  be  entirely  disregarded. 

28.  The  amount  of  the  attraction  of  any  two  bodies  for  each 
oJJiej^will  be  proportional  to  their  respective  quantities  of 
matter.  \Masses  of  matter,  therefore,  on  the  surface  of  the  earffip 
have  an\  attraction  for,  or  gravitate  towards,  each  other*;  but 
the  attraction  of  the  eajrth  is  at  the  same  time  so  much  greater, 
in  consequence  of  its  greater  quantity  of  matter,  that  their 
attraction  for  each  other  is  quite  insensible.  Still,  bodies  at 
the  surface  of  the  earth  do  exert  an  influence  on  each  other ; 

Quest.  27.  Will  two  plumb-lines  near  each  other  be  parallel  ?  If  two 
plumb-lines  are  suspended,  one  at  Philadelphia,  and  the  other  at  Utica  in 
the  State  of  New  York,  which  is  nearly  on  the  same  meridian  with  Phila- 
delphia, what  angle  would  they  make  with  each  other  ?  Would  the  error 
arising  from  considering  plumb-lines  parallel,  ordinarily  be  sensible  in  prac- 
tice ?  28.  To  what  will  the  amount  of  the  attraction  of  two  masses  of  matter 
for  each  other  be  proportional  ?  Why  is  not  the  attraction  of  two  masses  of 


Fig.  14. 


24 


NATURAL     PHILOSOPHY. 


and  it  has  been  found  that  the  plumb-line  by  the  side  of  a 
high  mountain  is  drawn  sensibly  out  of  its  true  perpendicular 
position. 

This  attraction  between  masses  of  matter,  as  in  all  other 
cases  where  force  is  exerted,  is  mutual ;  and  when  a  heavy 
body,  as  a  stone,  falls  towards  the  earth,  the  earth  also  falls 
towards  the  stone ;  but  the  distance  which  it  actually  passes 
through  will  be  as  much  less  than  that  passed  over  by  the 
stone,  as  its  mass  is  greater. 

29.  If  there  were  nothing  to  impede  the  free  motion  of  bodies 
near  the  earth's  surface,  all  falling  bodies  would  move  towards 
it  with  equal  velocity.  Daily  experience  seems  indeed  to  con- 
tradict this,  as  heavy  bodies  appear  to  fall  with  much  greater 
velocity  than  light  ones;  but  the  difference  is  caused  by  the 
resistance  of  the  atmosphere,  which  retards  light  bodies  more 
in  proportion  to  their  weight  than  it  does  heavy  ones.  That 
the  observed  difference  in  the  velocity  of  light  and  heavy  bodies 
falling  towards  the  earth  is  to  be  attributed  to  the  in- 
fluence of  the  atmosphere,  is  shown  conclusively  in  the 
well-known  experiment  of  letting  two  bodies  of  this 
kind,  as  a  feather  and  a  piece  of  coin,  fall  together  in  a 
tall  receiver  from  which  the  air  has  been  exhausted. 

The  experiment  may  be  performed  in  the  following 
manner.  Let  a  receiver  of  glass  (figure  15),  three 
inches  in  diameter,  and  four  or  five  feet  in  length,  con- 
tain a  feather  and  some  heavy  substance,  as  a  piece 
of  coin.  After  attaching  it  to  the  air-pump  and  ex- 
hausting the  air,  it  is  to  be  held  in  a  vertical  position 
and  then  suddenly  inverted,  so  that  the  bodies  may 
fall  from  end  to  end.  If  the  air  is  perfectly  exhausted, 
it  will  be  seen  that  both  bodies  fall  with  the  same 
velocity. 

30.  It  might  indeed  seem,  at  first  sight,  that,  inde- 
pendent of  the  retarding  influence  of  the  air.  heavy 
bodies  should  fall  more  rapidly  than  those  that  are 
lighter;  but  it  is  to  be  recollected  that  matter  of  itself 
is  entirely  inert,  and  that  consequently  the  force  re- 
quired to  set  a  mass  in  motion,  or  give  it  any  required 
velocity,  will  be  exactly  in  the  ratio  of  the  quantity 
of  matter.  Thus,  if  a  body  weighing  one  pound  falls  by 
Fig.  is.  the  force  of  gravity  with  a  given  velocity,  to  cause 

matter  for  each  other  near  the  surface  of  the  earth  perceptible  ?  Are  moun- 
tains capable  of  drawing  the  plumb-line  from  its  true  position  ?  Is  the  at- 
traction between  two  masses  always  reciprocal  ?  In  approaching  each  other, 
will  the  greater  or  smaller  mass  move  over  the  greater  distance  ?  29.  Do  all 
bodies  fall  towards  the  earth  with  equal  velocity  ?  Why  do  heavy  bodies,  in 
falling,  move  more  rapidly  than  light  ones  ?  How  may  it  be  shown  that,  but 
for  the  resistance  of  the  air,  both  heavy  and  light  bodies  would  fall  with  equal 
velocity  ?  30.  Should  it  require  more  force  to  set  a  heavy  body  in  motion 


MECHANICS.  25 

another  body  of  four  pounds'  weight  to  fall  with  the  same  velo- 
city will,  of  course,  require  the  exertion  of  four  times  as  much 
force.  They  should  therefore  fall  with  equal  velocities. 

31.  The  ascent  of  light  bodies,  as  smoke  and  vapor,  or  a 
balloon,  through  the  air,  furnishes  no  exception  to  the  univer- 
sality of  the  action  of  gravity,  but  is  in  strict  accordance  with 
it.    In  air  and  in  liquids,  the  particles  of  which  are  free  to  move 
among  themselves,  the  bodies  having  the  least  weight  in  pro- 
portion with  their  bulk,  will  be  forced  upward  by  the  greater 
gravitation  of  the  heavier.  Now  this  is  the  case  in  the  instances 
mentioned,  as  will  be  more  fully  explained  hereafter;  the  bal- 
loon, for  instance,  being  lighter  than  the  same  volume  of  air, 
is  forced  upward  by  the  tendency  of  the  air  to  fall  beneath  it 
and  occupy  its  place. 

32.  The  spherical  form  of  the  earth  and  planets  appears  to 
result  from  this  law  ;  for  all  the  parts  of  these  bodies  being 
equally  attracted  towards  the  centre  of  the  mass,  would  arrange 
themselves  at  equal  distances  around  it,  or,  in  other  words, 
the  mass  would  take  the  spherical  form. 

33.  Taking  advantage  of  this  property,  lead -shot  are  cast 
perfectly  spherical  in  form,  by  causing  the  globules  of  the  melt- 
ed metal  to  fall  from  the  tops  of  high  towers,  so  as  to  become 
solid  before  reaching  the  bottom.     The  attraction  of  the  parti- 
cles among  themselves  causes  the  mass  while  falling  through 
the  air  to  take  the  form  mentioned.     To  prevent  the  shot  from 
being  bruised  by  the  fall,  they  are  received  at  the  bottom  in  a 
cistern  of  water. 

34.  The  attraction  of  bodies  at  different  distances  is  inversely 
as  the  squares  of  those  distances.     This  seems  to  be  the  law 
which  regulates  the  action  of  all  forces  which  emanate  from  a 
centre,  and  spread  themselves  around.     If  two  bodies  at  the 
distance  of  a  foot  attract  each  other  with  a  force  equal  to  1, 
then  at  the  distance  of  two  feet  their  attraction  will  be  only  j, 
and  at  three  feet  distance  it  will  be  £,  &c. 

The  attraction  of  the  earth,  or  the  gravitation  of  bodies  to- 
wards it,  is  greatest  at  the  surface,  and  diminishes  as  we  ascend 

than  is  required  for  a  light  one  ?  Ought  a  body  weighing  one  pound  then  to 
fall  as  rapidly  as  one  weighing  four  pounds  ?  31.  Does  the  ascent  of  light 
bodies,  as  smoke  and  vapour,  furnish  any  exception  to  the  laws  of  gravity  as 
above  described  ?  How  is  the  ascent  of  these  bodies  explained  ?  32.  From 
what  does  the  spherical  form  of  the  earth  and  planets  result  ?  33.  How  are 
shot  cast  so  as  to  be  of  a  perfectly  spherical  form  ?  How  are  shot  pre- 
vented from  being  bruised  by  their  fall  ?  34.  How  does  this  force  vary 
with  the  distance  ?  If  two  bodies  at  the  distance  of  a  foot  attract  each  other 
with  a  force  equal  to  one,  what  will  be  their  attraction  at  the  distance  of  two 
feet?  At  the  distance  of  three  feet  ?  Where  is  the  attraction  of  the  earth 

freatest  ?     Above  the  surface,  how  does  the  earth's  attraction  decrease  ? 
'rom  what  point  is  the  distance  to  be  reckoned  ?    How  much  would  a  body 
weighing  a  pound  at  the  surface  weigh  at  the  height  of  4000  miles  ?    How  is 
this  result  obtained  ? 
3 


26  NATURAL      PHILOSOPHY. 

above  or  descend  below  it.  Above  the  surface,  the  attraction 
diminishes  according  to  the  law  just  stated,  the  distance  being 
reckoned  from  the  earth's  centre.  Thus,  if  we  call  the  semi- 
diameter  of  the  earth  4000  miles,  as  it  is  very  nearly,  then  at 
twice  this  distance,  or  8000  miles  from  the  centre,  a  body  that 
would  weigh  a  pound  at  the  surface  would  weigh  only  £  of  a 
pound  ;  and  at  12,000  miles  from  the  centre,  or  8000  miles  from 
the  surface,  it  would  weigh  only  ^  of  a  pound,  &c. 

35.  Below  the  surface,  the  force  of  gravity  diminishes  only 
as  the  distance ;  that  is,  a  body  weighing  a  pound  at  the  sur- 
face, at  the  distance  of  1000  miles  below,  or  one-fourth  of  the 
distance  to  the  centre,  would  weigh  only  f  of  a  pound ;  and 
2000  miles  below  the  surface,  it  would  weigh  only  i  a  pound, 
and  so  on. 

But  it  is  to  be  noticed  that  in  all  these  cases,  even  if  we  could 
find  means  to  transport  ourselves  to  the  places  supposed,  we 
could  not  make  use  of  the  ordinary  balance  to  determine  the 
truth  or  falsity  of  our  deductions;  for  the  weights  used  losing 
of  course  just  as  much  as  the  substance  weighed,  they  would 
balance  each  other  as  perfectly  at  any  of  these  positions  as  at 
the  surface.  At  the  distance  of  the  moon,  which  is  about 
240,000  miles,  or  60  semi-diameters  of  the  earth  from  us,  bodies 
would  weigh  only  ^TT  as  much  as  at  the  earth's  surface ;  yet 
bodies  that  would  counterpoise  each  other  at  the  earth  would 
of  course  do  the  same  at  the  moon.  The  torsion  balance,  to  be 
described  hereafter,  would  however  furnish  the  means  of  de- 
termining the  question. 

36.  As  the  earth  is  not  a  perfect  sphere,  and  all  parts  of  its 
surface  are  not  therefore  at  an  equal  distance  from  the  centre, 
the  force  of  gravity  must  vary  at  different  places,  being  less  at 
the  equator  than  at  the  poles ;  but  the  variation  is  inconsidera- 
ble, though  easily  determined  by  means  hereafter  to  be  de- 
scribed. 

37.  Centre  of  Gravity.  —  The  centre  of  gravity  of  a  body  is 
that  point  about  which  all  its  parts  will  be  equally  balanced  in 
every  position  of  the  body.    Consequently,  if  this  point  is  sup- 
ported by  mechanical  means,  the  body,  whatever  may  be  its 
form  or  position,  will  lie  at  rest. 

The  proper  idea  of  the  centre  of  gravity  will  readily  be  ob- 
tained by  considering  what  takes  place  when  an  attempt  is 
made  to  balance  a  straight  wire,  of  some  ten  or  twelve  inches 

Quest.  35.  How  does  the  force  of  gravity  diminish  below  the  surface  ?  If  a 
body  weighs  a  pound  at  the  surface,  how  much  will  it  weigh  1000  miles  be- 
low the  surface  ?  If  we  could  transport  ourselves  at  pleasure  to  places  above 
and  below  the  surface,  could  we  make  use  of  the  ordinary  balance  to  verify 
these  results  ?  Why  ?  What  balance  may  be  used  for  the  purpose  ?  36. 
Are  all  parts  of  the  earth's  surface  equally  distant  from  the  centre  ?  Is  the 
force  of  .gravity  of  equal  intensity  at  the  equator  and  at  the  poles  ?  37.  What 
is  the  centre  of  gravity  of  a  body  ?  How  may  a  correct  idea  of  the  centre  of 


MECHANICS.  27 

in  length,  on  the  back  of  a  knife.  Every  particle  of  the  wire  is 
drawn  downward  equally  by  the  earth's  attraction,  and  the 
wire  inclines  to  fell  one  way  or  the  other  until  it  is  made  to 
rest  exactly  upon  its  centre ;  then  the  attraction  of  the  particles 
on  one  side  of  the  knife,  being  precisely  equal  to  that  of  those 
on  the  other  side,  an  equipoise  will  be  produced,  and  the  wire 
will  be  supported.  This  point  at  which  it  is  supported  will  be 
the  centre  of  gravity  of  the  wire. 

In  bodies  of  a  regular  form  (as  the  circle,  square,  cube,  and 
sphere)  and  uniform  density,  this  point  is  always  found  exactly 
at  the  centre ;  but  this  is  not  the  case  if  the  form  is  irregular, 
or  if  some  parts  are  more  dense  than  others. 

38.  The  centre  of  gravity  of  many  bodies  which  are  com- 
posed of  the  same  kind  of  particles  is  found  without  difficulty. 
Thus,  the  centre  of  gravity  of  a  triangle  will  be  in  the  point 
where  two  lines,  drawn  from  the  vertices  of  two  of  its  angles 
to  the  middle  of  the  sides  opposite,  meet. 

*  In  the  triangle  ABC,  figure  16,  ac- 
cording to  what  has  been  said,  the  cen- 
tre of  gravity  must  be  somewhere  in  the 
line  B  E,  drawn  from  the  vertex  B  to  E, 
the  middle  point  of  the  side  A  C  oppo- 
site; and  it  must  also  be  somewhere  in 
the  line  C  D,  drawn  in  like  manner,  from 
the  vertex  C ;  but  as  it  must  be  in  both 
of  these  lines  at  the  same  time,  it  must 
Fig.  16.  be  at  S,  the  only  point  that  is  common 

to  the  two. 

39.  In  any  figure  bounded  by  straight  lines,  the  centre  of 
gravity  may  be  found  by  dividing  it  first  into  triangles,  and 
finding  the  centre  of  gravity  of  each,  and  then  finding  the  centre 
of  gravity  of  these  triangles  considered  as  separate  masses. 

Thus,  let  ABODE,  figure  17,  be 
the  body  in  question ;  divide  it  into  the 
three  triangles  A  B  C,  A  D  C,  and  A  D  E, 
and  find  the  centre  of  gravity  of  each 
as  already  described,  which  we  will 
suppose  to  be  the  points  a  b  and  c. 
Then  join  two  of  these  points,  as  a  and 
6,  by  the  line  a  b,  in  which  of  course 
will  be  the  centre  of  gravity  for  these 
two  triangles ;  and  the  exact  position 
of  this  point  will  be  as  much  nearer  to 
b  than  to  a,  as  the  triangle  ADC  is 

gravity  of  a  body  be  easily  obtained  ?  When  will  an  equipoise  of  the  wire 
be  produced  ?  In  bodies  of  a  regular  form  and  uniform  density,  where  is  the 
centre  of  gravity  ?  38.  How  may  the  centre  of  gravity  of  a  triangle  be 
found  ?  39.  How  may  the  centre  of  gravity  be  found  in  any  figure  which  is 
bounded  by  straight  lines  ? 


NATURAL     PHILOSOPHY 


greater  than  ABC.  We  will  suppose  it  to  be  at  d.  Then  join 
this  point  and  c,  and  in  this  line  proceed  to  find,  in  the  same 
manner  as  before,  the  point  e,  which  will  be  the  centre  of  gra- 
vity between  the  parts  A  D  C  B,  and  the  triangle  A  D  E,  or,  in 
other  words,  the  centre  of  gravity  of  the  whole  body. 

Though  we  have  spoken  of  the  centre  of  gravity  of  a  body 
as  being  a  point  in  the  body  itself,  yet  this  is  not  necessarily 
the  case.  In  a  ring  of  uniform  density,  for  instance,  the  centre 
of  gravity  will  be  at  the  centre  of  the  circle,  a  point  equally  dis- 
tant from  any  portion  of  the  solid. 

40.  When  a  body  is  suspended  by  a  cord  attached  to  some 
point  in  it,  its  centre  of  gravity,  when  it  is  at  rest,  will  always 
be  in  a  line  let  fall  perpendicularly  from  that  point. 

The  centre  of  gravity  of  an  irregular 
body,  considered  as  a  surface,  as  a  piece  of 
board,  A  BCD,  figure  18,  may  therefore  be 
found  as  follows.  Let  the  body  be  suspended 
by  some  point,  as  C ;  to  this  point  attach  a 
plumb-line  (§  27),  and  with  a  pencil  draw 
CD.  According  to  what  has  been  said,  the 
centre  of  gravity  of  the  body  musl  be  in 
this  line.  Then  suspend  the  body  by  an- 
other point,  A,  and  to  it  as  before  attach  the 
plumb-line,  and  draw  AB,  which  must  also 
contain  the  centre  of  gravity.  But  being  in 
both  of  these  lines,  it  "must  of  course  be  in 
their  common  intersection,  E;  and,  upon 
trial,  it  will  be  found  that  the  body  will  ba- 
lance itself  very  accurately  upon  this  point. 

Fig.  18. 

41.  If  the  body  be  not  of  uniform  density,  the  centre  of  gra- 
vity is  always  nearest  to  the  part  which  is  most  dense.     Thus, 
in  a  circle,  as  we  have  stated,  the  centre  of  gravity  is  at  its 
centre  if  its  density  be  uniform;  but  if  one  half  of  it  is  made  of 
wood,  and  the  other  half  of  lead,  which  is  heavier  than  wood, 
the  centre  of  gravity  of  the  whole  will  not  be  in  the  centre  of 
the  circle,  but  considerably  to  one  side  of  it  in  the  lead. 

42.  A  line  let  fall  perpendicularly  from  the  centre  of  gravity 
of  a  body  is  called  the  line  of  direction ;  and,  in  order  that  the 
body  may  be  supported,  this  line  must  always  fall  within  the 
base  on  which  it  rests.    If  it  falls  without  the  base,  the  body 
will  fall. 

Quest,  40.  When  a  body  is  suspended  by  a  cord  so  as  to  swing  freely, 
where  will  its  centre  of  gravity  be  ?  How  may  the  centre  of  gravity  of  an 
irregular  surface  be  found  ?  41 .  If  a  body  is  not  of  uniform  density,  towards 
what  part  of  it  is  its  centre  of  gravity  found  ?  42.  What  is  the  line  of  direc- 
tion of  a  body  ?  What  must  be  the  position  of  this  line  in  order  that  a  body 
may  stand  firm  ? 


MECHANICS. 


Thus,  the  body  A  B  C  D,  figure  19, 
whose  centre  of  gravity  is  at  S,  though 
inclined,  remains  firm,  because  the 
line  of  direction  falls  within  the  base 
CD;  but  if  we  place  upon  it  another 
piece,  A  E  F  B,  by  which  the  centre  of 
gravity  of  the  whole  body  will  be 
changed  to  S',  it  will  fall,  because  the 
line  of  direction  will  then  fall  without 
the  base. 

43.  In  Pisa  in  Italy  is  the  well- 
known  leaning  tower,  figure  20, 
which  inclines  15  or  16  feet  from  a 
perpendicular;   but  it  has  stood 
firm  in  this  position  many  hun- 
dred years,  the  line  of  direction, 
notwithstanding    its    inclination, 
still  falling  considerably  within  its 
base. 

44.  From  what  has  been  said, 
it  will  be  seen  the  stability  of  a 
body  will  depend  chiefly  on  two 
circumstances ;  its  height,  and  the 
extent  of  its   base.    A  pyramid 
stands  firm,  because  its  centre  of 
gravity  is  comparatively  low,  and 

^  its  base  is  very  extensive,  in  pro- 
|S  portion  to  its  magnitude.  On  the 
1=1  other  hand,  a  sphere  is  easily  put  in 
motion,  because  from  its  figure  it 
rests  upon  a  single  point;  and  if  the 
plane  which  supports  it  is  ever  so  little  inclined,  the  line  of  direc- 
tion will  fall  at  one  side  of  this  point,  as  is  shown  in  figure  21. 


Let  C  be  the  centre  of  the  sphere  of 
which  the  circle  BD  is  a  section ;  C  A 
will  be  the  line  of  direction  which  falls 
out  of  the  base  or  point  of  support,  this 
being  at  B.  Hence,  the  body  will  move 
down  the  plane. 


Fig.  20. 


Fig.  21. 


Quest.  43.  How  much  does  the  leaning  tower  in  Pisa  incline  from  a  per« 
pendicular  ?  Has  it  been  long  in  this  position  ?  44.  On  what  two  circum* 
stances  does  the  stability  of  a  body  chiefly  depend  ? 


Fig.  22. 


oU  NATURAL     PHILOSOPHY. 

45.  Whenever  a  body  is  made  to  move  by  the  force  of 
gravity,  its  centre  of  gravity  must  descend;  if  its  position  or 
form  is  such  that  any  change  of  position  would  require  this 
point  to  be  raised,  it  will  be  supported,  and  remain  at  rest. 
Hence,  a  mass  with  a  wide  base  may  be  supported  on  a  plane 
considerably  inclined. 

Thus,  a  cube  of  metal, 
or  other  heavy  body,  as 
A  B,  figure  22,  is  supported 

s x       ,,         x       ^         on  the  inclined  plane  C  D, 
/    \     /•      ^>^^  notwithstanding     the    in- 

clination of  the  plane ;  for 
if  it  moves,  its  centre  of 
gravity  must  still  be  raised 
and  made  to  pass  through 
the  arc  EP  of  a  circle. 
But  it  is  to  be  observed 
here  that  the  body  is  sup- 
posed to  roll  and  not  slide.  If  the  friction  of  the  body  on  the 
plane  is  small,  it  may  slide  down  the  plane,  which  of  course  will 
be  entirely  independent  of  any  property  of  the  centre  of  gravity. 

46.  Man,  when  erect,  stands  less  firmly  than  most  other  ani- 
mals, because  the  base,  composed  of  his  two  feet,  is  small,  and 
his  centre  of  gravity  is  very  high  above  it.  (§  44.)    Hence,  it 
requires  no  little  dexterity  in  the  child  to  learn  to  walk ;  and  it 
is  a  long  time  before  he  acquires  sufficient  experience  to  enable 
him  at  all  times  to  preserve  his  centre  of  gravity,  by  keeping 
the  line  of  direction  within  the  base,  as  he  balances  himself  first 
upon  one  foot  and  then  upon  the  other. 

47.  A  man  carrying  a  burden  upon  his  back  naturally  leans 
forward ;  and  when  carrying  it  on  one  shoulder  he  leans  to- 
wards the  other  side.  Rope-dancers,  in  order  to  balance  them- 
selves the  more  readily,  hold  in  their  hands  a  long  pole,  loaded 
at  each  end,  which  enables  them  the  more  easily  to  change 
their  centre  of  gravity  by  moving  the  pole  in  one  direction  or 
another,  as  may  be  necessary  to  preserve  them  from  falling. 

48.  Little  James  had  a  twenty-five  cent  piece  offered  him  if  he 
would  place  his  back  firmly  against  the  door,  and  stoop  down 
and  pick  the  money  up  from  the  carpet,  when  thrown  down  im- 


Why  does  a  pyramid  stand  firm  ?  Why  is  a  sphere  easily  put  in 
motion  when  resting  on  an  inclined  plane  ?  45.  What  must  take  place  with 
regard  to  the  centre  of  gravity  of  a  body,  when  it  is  moved  by  the  force  of 
gravity  ?  How  does  the  centre  of  gravity  of  a  cube  move  when  it  is  turned 
over,  even  though  it  may  rest  on  a  plane  somewhat  inclined  ?  46.  Why 
does  man,  when  erect,  stand  less  firmly  than  most  other  animals  ?  47.  Why 
does  a  man,  when  carrying  a  burden  upon  his  back,  lean  forward  ?  If  hrs 
burden  is  upon  one  shoulder,  why  does  he  lean  towards  the  other  side  ?  By 
what  means  do  rope-dancers  balance  themselves  upon  the  rope  ?  48.  Why 
could  not  little  James  stoop  down  to  pick  up  the  piece  of  money  on  the  floor 
before  him,  when  standing  in  the  position  described  ? 


MECHANICS. 


31 


mediately  before  him ;  but  after  many  trials  he  found  it  impos- 
sible, and  was  obliged  to  give  it  up,  wondering  greatly  what 
could  be  the  reason.  If  he  had  studied  this  subject,  he  would 
have  known  that  when  a  person  stoops^forward  he  is  obliged 
to  throw  his  body  backward,  so  that  his  centre  of  gravity  may 
be  supported ;  but  this  being  impossible  in  the  present  case,  in 
consequence  of  his  back  being  against  the  door,  he  could  not 
stoop  enough  to  reach  the  floor  without  pitching  forward. 

The  same  youth  had  a  miniature  horse  which  he  was  accus- 
tomed to  stand  on  the  edge  of  the  table  on  his  hind  feet,  as 
though  he  would  make  him  pitch  off  upon  the  floor;  but  under 
the  horse  from  his  breast  proceeded  a  stiff  wire  with  a  heavy 
weight  at  the  end,  so  that  the  centre  of  gravity  of  the  whole 
fell  under  the  table.  The  particular  manner  in  which  the  horse 
was  supported  allowed  it  to  vibrate  considerably  backward 
and  forward,  as  though  he  were  rearing. 

49.  The  shape  of  bodies  may  sometimes  be  so  contrived  as 
to  make  them  appear  to  rise  when  they  are  actually  falling. 
The  case  of  the  double  cone  rolling  up  an  inclined  plane  is 
often  referred  to. 

The  body  E  F,  figure  23,  consist- 
ing of  two  equal  cones  united  by 
their  bases,  is  placed  upon  two 
straight  and  smooth  rulers,  AB 
and  C  D,  which  at  one  end  meet  at 
Fi  23  a  small  angle,  and  rest  upon  the 

table,  but  at  the  other  are  raised  a 

little  above  the  table.  The  double  cone  will  roll  towards  the 
elevated  end  of  the  rulers,  and  will  have  the  appearance  of 
ascending;  but,  from  its  peculiar  form,  it  is  manifest  upon 
examination  that,  on  the  contrary,  it  is  falling.  To  make  this 
plain,  it  will  only  be  necessary  to  hold  a  ruler  parallel  to  the 
table  over  the  rolling  body,  and  as  it  advances  it  will  be  seen 
to  fall  more  and  more  from  it. 

50.  So  a  circle  of  wood,  or  some  other  light  substance,  may 
be  made  to  move  a  short  distance  up  an  inclined  plane  by 
making  one  side  heavier  than  the  other,  and  placing  it  properly 
on  the  plane. 

Let  A  B,  figure  24,  be  a  circle  of  wood 
situated  on  an  inclined  plane,  having  a 
piece  of  lead  B  attached  to  it  near  the 
circumference ;  it  will  roll  up  the  plane, 
the  whole  wheel  actually  rising,  until 
the  weight  B  has  nearly  reached  the 
lowest  point,  when  it  will  stop.  It 
might  at  first  seem  that  the  wheel  has 

Quest.  49.  How  may  a  solid  in  the  shape  of  a  double  cone  be  made  to  roll 
up  an  inclined  plane  ?  Does  the  centre  of  gravity  of  the  body  ascend  ?  50. 
How  may  a  circle  of  wood  be  made  to  rise,  by  its  own  gravity,  a  distance  on 
an  inclined  plane  ? 


Fig.  24. 


32  NATURAL     PHILOSOPHY. 

really  raised  itself;  but  though  its  whole  mass  has  risen,  the 
centre  of  gravity,  which  we  will  suppose  at  C,  has  fallen.  If 
now  it  is  desired  to  roll  the  wheel  farther  up  the  plane,  it  is 
manifest  that  a  greater  effort  will  be  required  than  if  it  had  not 
been  loaded;  but  after  the  weight  B  has  passed  the  highest 
point,  it  will  move  on  as  before  of  its  own  accord. 


MOTION     AND     FORCE. 

51.  By  the  motion  of  a  body  we  mean  its  change  of  place, 
which,  in  consequence  of  its  inertia,  as  we  have  seen  (§  9),  can 
take  place  only  by  the  application  of  some  force.     So  also  by 
force  we  understand  the  power  which  produces  motion,  or  has 
a  tendency  to  produce  it. 

52.  Motion  may  be  absolute  through  space,  or  one  body  may 
have  a  motion  relatively  to  another,  which  may  itself  be  at  rest 
or  in  a  state  of  motion.    But  we  know  nothing  of  any  other 
than  relative  motion,  and  to  this  only  therefore  will  our  re- 
marks be  confined. 

53.  The  degree  of  rapidity  with  which  a  body  moves  is  its 
velocity,  which  may  be  uniform,  as  when  the  body  passes  over 
equal  spaces  in  equal  times ;  or  it  may  be  accelerated,  as  when 
the  portions  of  space  passed  over  in  equal  times  increase ;  or 
retarded,  as  when  the  spaces  passed  over  in  equal  times  dimi- 
nish. When  this  increase  or  diminution  is  constant,  the  velocity 
is  said  to  be  uniformly  accelerated  or  retarded. 

54.  It  has  already  been  stated  (§  9),  that  a  body  once  put  in 
motion  would  continue  to  move  for  ever,  unless  stopped  by 
some  force ;  or,  in  other  words,  that  it  would  never  stop  itself. 
But  an  experiment  of  this  kind  of  course  was  never  made;  we 
every  day  see  bodies  in  motion,  some  indeed  moving  with  im- 
mense speed,  but  all  alike  soon  come  to  a  state  of  rest.    This 
is  because  of  the  resistance  they  constantly  meet  with.    This 
resistance  arises  from  several  causes,  as  the  resistance  of  the 
air,  the  constant  action  of  gravity,  and  friction.  The  resistance 
occasioned  by  friction  is  slight  on  bodies  projected  through  the 
air,  as  a  cannon  ball ;  but  it  is  very  great  on  bodies  moving 
over  rough  surfaces,  as  the  surface  of  the  earth.    Some  solids, 
as  ice,  occasion  comparatively  but  little  friction,  though  it  is 
impossible  to  find  a  body  which  opposes  no  resistance  from 
this  cause. 

Quest.  51.  What  is  meant  by  motion  ?  By  what  must  motion  be  produced  ? 
52.  What  is  absolute  motion  ?  What  is  relative  motion  ?  53.  What  is  velo- 
city ?  When  is  motion  said  to  be  uniform  ?  When  is  it  said  to  be  accelerated  ? 
When  retarded  ?  When  is  motion  said  to  be  uniformly  accelerated  or  re- 
tarded ?  54.  Why  does  a  body  when  put  in  motion  by  man  always  come  in 
a  short  time  to  a  state  of  rest  ?  What  occasions  the  resistance  ?  Is  the  re- 
sistance of  the  air  considerable  ? 


MECHANICS.  33 

55.  The  resistance  occasioned  by  friction,  though  sometimes 
producing  great  inconvenience,  is  often  made  use  of  for  im- 
portant purposes.     It  is  by  the  friction  of  the  driving-wheels 
of  a  locomotive  on  the  rails  that  it  is  made  to  move  on  a  rail- 
road, frequently  drawing  after  it  an  immense  load.     These 
wheels  are  made  to  revolve  by  the  engine ;  but  this  would  not 
put  the  cars  in  motion,  it  is  evident,  were  it  not  for  their  great 
friction  upon  the  rails ;  hence  the  rails  must  always  be  kept 
free  from  ice  and  snow,  which  would  destroy  or  greatly  dimi- 
nish the  friction,  and  cause  the  driving-wheels  merely  to  revolve 
upon  the  rails,  without  putting  the  train  in  motion.  Sometimes 
this  is  seen  when  the  wheels  of  a  locomotive  are  started  sud- 
denly, especially  if  it  is  attached  to  a  heavily  loaded  train ;  for 
a  moment  the  wheels  slide  upon  the  rails  as  they  revolve,  but 
the  train  soon  starts  and  moves  onward. 

Friction  is  also  made  use  of  to  check  the  motion  of  a  train 
of  cars  upon  a  rail-road,  or  to  stop  it.  This  is  done  by  means 
of  a  brake,  which  consists  of  a  combination  of  levers  by  which 
heavy  pieces  of  iron  are  made  to  press  firmly  against  the  rims 
of  several  of  the  wheels,  thus  gradually  checking  their  motion. 
It  is  necessary  that  it  should  be  done  gradually,  as  the  sudden 
stopping  of  the  train  when  in  rapid  motion  would  be  produc- 
tive of  injury. 

56.  The  resistance  occasioned  by  friction  is  seen  when  a 
person  jumps  from  a  carriage  in  rapid  motion.     When  his  feet 
strike  the  ground  he  is  in  danger  of  being  thrown  down,  be- 
cause the  friction  upon  the  surface  is  so  great  as  to  bring  them 
at  once  to  a  state  of  rest,  while  his  body  tends  to  move  onward 
as  before.    If  the  carriage  were  moving  on  smooth  ice,  by  care- 
fully jumping  upon  it  the  danger  would  be  less,  as  it  would 
allow  his  feet  to  glide  over  it  a  distance  before  coming  to  a 
state  of  rest. 

57.  The  resistance  of  the  atmosphere  is  much  the  greatest 
when  the  motion  is  rapid ;  when  one  moves  his  hand  slowly 
through  the  air,  its  presence  is  scarcely  felt;  but  if  he  moves  it 
rapidly,  the  resistance  is  plainly  perceived.     The  experiment 
will  appear  more  decisive  to  the  young  learner  by  holding  an 
expanded  fan  in  his  hand  when  waving  it  in  the  air.     The  re- 
sistance-of  the  air  to  cannon-balls,  which  are  projected  through 
it  with  immense  velocity,  is  very  great. 

Quest.  55.  Is  the  resistance  of  friction  sometimes  made  use  of  for  impor- 
tant, purposes  ?  How  are  locomotives  made  to  move  on  a  railway  ?  Why 
must  the  rails  in  winter  be  kept  free  from  ice  ?  How  is  the  motion  of  the 
locomotive  and  the  cars  checked  when  necessary  ?  56.  Why  is  a  person 
liable  to  be  thrown  down  on  alighting  from  a  carriage  in  rapid  motion  ?  What 
would  be  the  effect  if  the  carriage  were  moving  over  smooth  ice,  and  the  per- 
son should  jump  carefully  upon  the  surface  ?  57.  When  is  the  resistance  of 
the  air  greatest  ?  What  is  the  effect  of  moving  a  fan  rapidly  through  the  air  ? 
What  is  said  of  the  resistance  of  the  air  upon  cannon-balls  when  projected 
with  great  velocity  ? 


34  NATURAL     PHILOSOPHY. 

58.  The  effect  of  gravitation  is  to  bring  a  body  in  motion  to 
the  earth,  which  by  its  friction  soon  causes  it  to  come  to  a  state 
of  rest,  however  rapid  may  have  been  its  motion. 

59.  In  any  given  case,  the  velocity  with  which  a  body  will 
move,  other  things  being  equal,  will  depend  upon  the  force 
with  which  it  is  impelled,  and  will  be  in  the  direction  in  which 
the  force  has  acted.     Two  bodies  of  different  weights  will  re- 
quire forces  inversely  proportional  to  their  weights  to  give 
them  the  same  velocity  (§  30) ;  and  of  two  bodies  having  the  same 
weight,  one  will  move  with  twice  the  velocity  of  the  other,  if  it 
be  propelled  with  double  the  force. 

60.  Every  force  must  always  act  equally  in  opposite  direc- 
tions.   If  a  person  press  against  the  table  with  his  hand,  the 
table  opposes  a  precisely  equal  resistance  to  his  hand.  A  horse 
drawing  a  load  forward  is  pulled  backward  by  the  load  with  an 
equal  force.    A  bird  flying  in  the  air  strikes  it  with  its  wings, 
and  the  reaction  of  the  air  is  sufficient  to  sustain  the  weight  of 
its  body.    In  firing  a  rifle,  the  explosion  of  the  powder,  which 
gives  the  ball  its  velocity,  also  causes  the  recoil  of  the  piece ; 
and!  if  it  were  no  heavier  than  the  ball,  and  were  not  held  in  its 
place,  it  would  take  the  same  velocity  as  the  ball,  but  would 
move  in  the  opposite  direction. 

If  two  boats  of  similar  weight  and  form  were  on  a  smooth 
lake,  and  a  man  in  one  should  pull  upon  a  rope  held  by  a  per- 
son in  the  other,  both  would  have  to  make  the  same  exertion, 
and  both  boats  would  move  with  equal  velocity;  but  if  one  of 
the  boats  had  been  anchored,  and  therefore  remained  at  rest, 
the  man  in  it  holding  the  rape  would  have  been  obliged  to 
make  the  same  exertion. 

61.  This  principle  of  motion  or  force  is  sometimes  expressed 
by  saying  that  action  and  reaction  are  always  equal,  and  in 
opposite  directions. 

62.  Motion  is  sometimes  reflected ;  that  is,  a  moving  body 
strikes  another  that  is  fixed,  and  is  thrown  back  or  rebounds 
in  an  opposite  direction.    If  an  elastic  body,  as  a  ball,  strike  a 
plain  surface  perpendicularly,  it  rebounds  perpendicularly ;  that 
is,  it  is  thrown  back  in  the  same  path  it  first  took ;  but  if  it 

Quest.  58.  How  does  gravitation  act  upon  bodies  in  motion  ?  59.  Upon 
what  will  the  velocity  of  a  body  depend  ?  When  will  two  bodies  of  different 
weights  move  with  the  same  velocity  ?  60.  Must  a  force  always  act  equally 
in  opposite  directions?  When  a  person  presses  with  his  hand  upon  a  table, 
what  opposing  force  is  there  ?  How  is  a  bird  supported  in  the  air  ?  Why 
does  a  cannon  or  rifle  recoil  when  fired  ?  If  the  piece  were  no  heavier  than 
the  ball,  and  unconfined,  what  would  be  the  effect  ?  How  is  this  principle 
illustrated  by  two  boats  on  a  smooth  lake  pulled  together  by  persons  in  them 
by  a  rope  ?  61.  How  is  this  principle  of  motion  or  force  sometimes  express- 
ed ?  62.  When  is  motion  said  to  be  reflected  1  What  is  the  angle  of  meri- 
dian and  the  angle  of  reflection  ?  How  do  these  angles  compare  with  each 
other  in  magnitude  ? 


MECHANICS.  35 

strikes  the  plane  obliquely,  it  rebounds  with  an  equal  obliquity, 
but  in  an  opposite  direction. 

The  law  is  as  follows:  Let  BE, 
figure  25,  be  a  plane  surface,  against 
which  an  elastic  ball,  A,  is  supposed 
to  move  in  the  direction  A  C,  striking 
it  at  C ;  it  will  then  rebound  in  the 
direction  of  C  F  with  the  same  velo- 
city as  before.  If  now  at  the  point 
C  we  make  C  G  perpendicular  to  B  E, 
it  will  be  found  that  the  angle  A  C  G, 
called  the  angle  of  incidence^  exactly 
equal  to  the  angle  GC  F,  called  the  angle  of  reflection. 

63.  A  single  force  acting  upon  a  body  can  give  it  motion  only 
in  a  straight  line  (§  59) ;  two  forces  are  necessary  to  produce 
curvilinear  motion. 

If  two  forces  act  upon  a  body  at  the  same  time,  the  body  will 
move  in  a  diagonal  between  them. 

_  Thus,  let  A,  figure  26,  be  a  body  acted 

on  at  the  same  instant  by  two  equal 
1C  forces  at  right  angles  to  each  other,  one 
i  of  which  would  cause  it  to  move  to  C  in 
i  the  time  the  other  would  cause  it  to  move 
j  to  E ;  instead  of  taking  either  of  these 
j  courses,  it  will  move  through  the  dotted 
j  line  to  G.  To  show  more  particularly 
j,,  that  this  would  be  the  case,  let  us  suppose 
B  to  C  is  east,  and  from  D  to  E 


? 

is  south ;  the  effect  of  the  force  B  alone 
then  would  be  to  drive  the  body  east  a  given  distance,  as  from  A 
to  C  in  a  second ;  and  the  effect  of  the  force  D  alone  to  drive  it 
the  same  distance  south,  as  from  A  to  E,  in  that  time.  Now,  it 
is  evident  that  neither  of  these  forces  would  in  any  degree 
counteract  the  effect  of  the  other ;  and  if  both  act  at  the  same 
time,  the  body  must  move  with  the  same  velocity  both  east  and 
south ;  that  is,  it  must  move  through  the  diagonal  A  G,  which 
is  called  the  resultant  of  the  two  forces.  Evidently  it  is  the 
diagonal  of  a  square.  The  body  at  the  end  of  the  second  will 
be  in  the  same  place  as  if  the  forces  had  acted  successively, 
causing  the  body  to  move  first  to  C  or  E,  and  then  to  G. 

When  the  two  forces  are  unequal,  the  direction  the  moving 
body  will  take  may  be  readily  determined. 

Quest.  63.  How  will  a  body  move  when  propelled  by  a  single  force  ?  How 
will  a  body  move  when  acted  upon  at  the  same  time  by  two  forces  ?  What 
is  the  line  in  which  the  body  moves  called  ?  How  may  the  resultant  be 
found  when  the  two  forces  are  unequal  ? 


36  NATURAL     PHILOSOPHY. 

Let  A,  figure  27,  be  a  body  acted  upon 
by  two  forces  in  the  direction  of  A  B  and 
3  AC.    Suppose  that  the  force  acting  in  the 
direction  of  A  B  is  equal  to  three,  and  that 
in  the  direction  of  AC,  to  two.    Make  the 

D| ^  |ine  A  B  equ-al  to  three,  and  A  D  equal  to 

e|  two,  and  parallel  to  these  draw  the  lines 

Fig.  27  D  E  and  B  E ;  then  join  A  E,  and  this  line 

will  be  the  path  taken  by  the  body  A.     It 
is  therefore  the  resultant  of  the  forces  AB  and  AD. 

64.  If  the  forces  act  at  some  other  angle  than  a  right  angle, 
their  resultant  may  be  found  in  a  similar  manner.    If  there  are 
more  than  two  forces  acting  upon  the  body,  the  resultant  of 
two  of  them  may  be  first  found,  and  then  the  resultant  of  this 
as  a  separate  force,  and  a  third  force,  and  so  on  with  all  the 
forces. 

These  cases  are  not  merely  theoretical ;  they  are  every  day 
actually  occurring.  As  an  instance  of  two  forces  acting  at  right 
angles,  suppose  a  boatman  rowing  his  canoe  across  a  stream. 
He  attempts  to  put  his  boat  directly  across,  but  the  current 
sets  him  downward;  and  before  he  reaches  the  opposite  bank, 
he  finds  he  is  far  below  the  point  from  which  he  started.  If  the 
stream  ran  south,  and  he  attempted  to  cross  from  the  east  to 
the  west  side,  supposing  the  force  exerted  by  the  boatman  pre- 
cisely equal  to  that  of  the  current,  it  would  be  found  on  exami- 
nation he  had  proceeded  exactly  in  a  south-west  direction. 
This  would  be  the  exact  resultant  of  the  two  forces  by  which 
the  boat  would  be  moved.  In  order  that  the  boat  might  pro- 
ceed directly  across  the  river  from  east  to  west,  it  would  be 
necessary  for  the  boatman  to  propel  his  boat  constantly  in  the 
direction  of  north-west. 

A  steam- vessel,  whose  paddles  tend  to  propel  her  northward, 
whilst  the  wind  blows  her  to  the  eastward,  and  the  tide  is  run- 
ning in  a  third  direction,  is  an  instance  of  the  action  of  these 
forces.  The  vessel  cannot  of  course  obey  all  the  forces  simul- 
taneously, and  takes  a  course  which  is  their  true  resultant. 

65.  The  combination  of  several  motions  sometimes  produces 
results  that  at  first  appear  a  little  singular.     A  person  riding 
rapidly  in  the  open  air  feels  the  drops  of  rain  strike  him  in  the 
face,  although  the  drops  may  be  falling  perpendicularly ;  and 

Quest.  64.  May  the  resultant  be  found  in  a  similar  manner  when  the  forces 
do  not  act  at  right  angles  to  each  other  ?  How  may  the  resultant  be  found 
when  there  are  more  than  two  forces  acting  together  ?  Do  instances  actually 
occur  in  which  two  or  more  forces  act  together  ?  If  a  man  should  attempt  to 
cross  a  river,  the  current  of  which  ran  south,  in  what  direction  would  he  move 
by  propelling  his  boat  directly  from  east  to  west  ?  In  what  directiqn  must 
he  shape  his  course  in  order  to  pass  directly  across  the  river  ?  65.  Why  does 
a  person  riding  rapidly  in  the  rain  feel  the  drops  strike  him  in  the  face  when 
they  are  falling  perpendicularly  ?  How  will  the  drops  appear  to  him  to  be 


MECHANICS 


37 


the  drops  will  appear  to  him  as  though  they  came,  not  perpen- 
dicularly downward,  but  considerably  inclined  towards  him. 
A  person  attempting  to  throw  a  ball  to  another  passing  rapidly 
in  a  rail-road  car,  would  throw  it,  not  directly  at  him,  but  at  a 
point  on  the  road  considerably  in  advrance  of  the  car  at  the 
time;  and  though  thrown  directly  towards  the  line  of  the  track 
on  which  the  car  is  moving,  to  the  person  in  the  car  it  will  ap- 
pear to  come  from  a  point  considerably  in  advance  of  him,  and 
at  an  angle  considerably  inclined  from  a  perpendicular  to  the 
line  of  the  road. 

A  heavy  body  let  fall  from  the  mast-head  of  a  ship  in  full  sail 
will  appear  to  fall  precisely  as  it  would  if  the  ship  was  at  rest, 
and  will  strike  the  deck  at  the  same  distance  from  the  mast ; 
for,  having  the  same  motion  as  the  ship  at  the  beginning  of  its 
descent,  it  will  appear,  all  the  time  it  is  falling,  at  the  same  dis- 
tance from  the  mast,  though  the  line  of  its  descent  is  in  reality 
a  curve. 

66.  Curvilinear  Motion.  —  Curvilinear  motion  is  always  the 
result  of  two  or  more  forces,  generally  but  two.  These  are 
called  the  centripetal  and  the  centrifugal  forces.  By  the  former, 
the  body  is  drawn  towards  the  centre ;  by  the  latter,  it  tends 
to  fly  from  the  centre  in  a  straight  line,  which  is  a  tangent  to 
the  circumference  of  the  curve  in  which  the  body  moves. 

jj  67.  If  a  ball  of  some  heavy  sub- 

"G-  stance  is  fixed  to  a  cord,  and  made 
to  revolve  rapidly  by  holding  the 
other  end  of  the  cord  in  the  hand, 
while  it  is  revolving,  its  tendency 
to  fly  off  is  plainly  felt  in  its  pull- 
ing, so  to  speak,  upon  the  cord ; 
and  if  now  the  cord  should  be 
broken,  it  will  fly  off  in  a  straight 
line.  In  this  case  the  cord  may  re- 
present the  centripetal  force,  and 
the  force  by  which  the  ball  tends 
to  break  the  cord,  the  centrifugal 
force.  In  figure  28,  let  A  be  some 
Fis-  ^  heavy  body  revolving  around  the 

centre,  S,  in  the  circumference  ABE;  if,  while  it  is  in  rapid 
motion,  just  as  it  arrives  at  the  point  A,  the  cord  C  is  suddenly 

falling  ?  Suppose  a  person  standing  by  the  side  of  a  rail-road  wishes  to  throw 
a  ball  to  another  person  passing  in  a  car  on  the  road  :  how  would  he  throw 
it  ?  Will  a  heavy  body  falling  from  the  mast-head  of  a  ship  when  sailing 
strike  the  deck  at  the  same  distance  from  the  mast  as  it  would  if  the  ship 
was  not  in  motion  ?  How  is  this  fact  explained  ?  66.  How  many  forces  are 
necessary  to  produce  curvilinear  motion  ?  Which  way  does  the  centripetal 
force  tend  to  move  the  body  ?  67.  If  a  heavy  body  is  whirled  rapidly  round 
by  means  of  a  cord,  what  will  represent  the  centripetal,  and  what  the  centri- 
fugal force  ?  If  the  cord  should  be  cut  as  the  body  is  revolving,  in  what 


38  NATURAL     PHILOSOPHY. 

cut  with  a  sharp  knife,  it  will  at  once  fly  off  by  its  centrifugal 
force  in  the  straight  line,  AF,  which  is  called  a  tangent  (§  69) 
to  the  circle.  If  the  cord  was  cut  when  it  was  at  the  point  B,  it 
would  take  the  direction  B  G,  which  is  also  a  tangent  at  the 
point  B.  So  if  the  cord  was  cut  when  the  revolving  body  was 
at  any  other  point,  the  body  would  fly  off  in  a  straight  line,  which 
would  be  a  tangent  to  the  circle  at  that  point. 

Boys  take  advantage  of  this  force  in  throwing  stones  with  a 
sling.  The  sling  is  so  constructed  that  the  stone  is  first  made 
to  revolve  rapidly,  so  as  to  give  it  a  great  centrifugal  force,  and 
then  is  suddenly  let  go,  by  which  a  great  velocity  is  communi- 
cated to  it. 

Drops  of  water  flying  from  a  wheel  that  is  turning  rapidly 
furnish  another  instance  of  the  operation  of  the  same  force. 
Grindstones,  and  even  strong  iron  wheels,  have  been  broken 
in  pieces  in  this  manner,  simply  by  causing  them  to  revolve  so 
rapidly  that  the  centrifugal  force  of  their  outer  parts  becomes 
so  great  as  to  tear  them  asunder. 

The  same  principle  explains  the  well-known  fact  that  a  bucket 
of  water  may  be  swung  over  the  head,  so  as  to  turn  the  top 
downward,  without  spilling  the  water ;  the  centrifugal  force  of 
the  water,  when  whirled  rapidly,  becomes  sufficient  to  overcome 
entirely  its  gravitation. 

68.  When  an  equestrian  is  riding  in  a  circle,  both  horse  and 
rider  are  seen  to  incline  considerably  inward;  this  is  to  coun- 
teract the  centrifugal  force  of  their  bodies,  which  often  becomes 
very  great,  especially  if  the  circle  is  small,  and  their  motion 
rapid.     But  carriages  not  having  this  power  to  make  compen- 
sation for  the  disturbing  force  thus  called  into  existence,  are 
often  overturned  when  an  attempt  is  made,  as  in  turning  a 
corner,  to  change  suddenly  the  direction  of  their  motion.  They 
will  of  course  always  fall  outward,  or  from  the  corner  around 
which  they  are  turning. 

69.  We  have  magnificent  examples  of  the  exact  balancing 
of  these  two  forces  in  the  continued  revolution  of  the  various 
bodies  of  the  solar  system.    The  earth  and  planets  are  con- 
stantly moving  around  the  sun  as  a  centre;  some  of  these  also 
at  the  same  time  serving  as  centres  around  which  other  smaller 
bodies  revolve,  called  satellites,  or  moons.    At  every  point  in 

direction  will  it  move  ?  How  do  boys,  in  throwing  stones  with  a  sling, 
take  advantage  of  the  centrifugal  force  ?  Why  does  water  fly  off  from  the 
rim  of  a  wheel  when  it  is  made  to  revolve  rapidly  ?  Is  there  any  danger  in 
making  grindstones  revolve  with  great  velocity  ?  When  a  bucket  of  water 
is  swung  over  the  head,  why  does  not  the  water  fall  out  as  the  bucket  passes 
bottom  upward  over  the  head  ?  68.  Why  does  a  horse,  when  running  in  a 
circle,  incline  inward  ?  Why  is  a  carriage  in  rapid  motion  in  danger  of  being 
overturned  in  passing  a  corner  ?  69.  Where  may  be  found  magnificent  ex- 
amples of  the  exact  balancing  of  the  centripetal  and  centrifugal  forces? 
Around  what  central  body  do  the  earth  and  planets  revolve  ?  Around  what 
body  does  the  moon  revolve  ?  Why  do  not  their  bodies  fly  off  into  space  ? 


MECHANICS. 


39 


their  orbits,  these  bodies  tend  to  rush  off  into  infinite  space  in 
straight  lines,  as  above  described  (§  67),  but  are  constantly  held 
in  by  the  attraction  of  the  central  body. 

70.  The  form  of  the  earth  itself  presents  a  remarkable  in- 
stance of  the  effects  of  the  centrifugal  force  produced  by  its 
rotation  on  its  own  axis.  The  motion  of  the  earth's  surface  at 
the  equator  by  its  rotation  on  its  axis,  is  about  thirteen  and  a 
half  miles  a  minute,  by  which  a  tendency  is  produced  in  the 
parts  about  it  to  fly  off  into  space,  like  drops  of  water  from  a 
revolving  wheel ;  but  this  result  is  prevented  by  the  strong  at- 
traction of  the  mass  of  the  earth  acting  from  the  centre,  which 
constitutes  the  centripetal  force  of  the  parts.  Still  the  effect  of 
the  centrifugal  force  is  seen  in  the  enlargement  of  the  earth  at 
the  equator,  the  equatorial  diameter  being  several  miles  greater 
than  the  polar  diameter. 


This  alteration  of  the  figure  of  the  earth 
is  easily  illustrated  by  the  apparatus  repre- 
sented in  figure  29.  On  a  perpendicular  axis, 
A  D  B,  are  two  thin  brass  hoops,  which  are 
fixed  to  the  axis  at  A,  but  are  loose  at  B. 
Now,  when  these  hoops  are  made  to  turn 
rapidly  by  means  of  the  handle,  C,  they  be- 
come flattened  in  the  direction  of  A  B  by 
the  part  at  B  rising,  and  enlarged  in  the  op- 
posite direction  EF.  This  is  occasioned  by 
\  the  centrifugal  force  of  the  parts  at  E  and  F. 


Fig.  29. 


LAW    OF    FALLING    BODIES. 

71.  The  fall  of  bodies  to  the  earth  when  unsupported,  is,  as 
we  have  seen  (§  24),  an  effect  of  the  earth's  attraction,  or  gra- 
vitation. This  motion  of  bodies,  as  every  one  has  noticed,  is 
not  uniform;  it  increases  rapidly  as  the  body  descends.  If  a 
lead  bullet  is  dropped  from  the  hand,  it  may  be  caught  again 
if  the  effort  is  made  instantly,  as  its  motion  is  at  first  slow;  but 
its  velocity  soon  increases  so  as  to  carry  it  beyond  the  reach ; 
and  if  the  hand  could  be  extended  to  it  after  it  has  fallen  a  few 
seconds,  it  would  be  dangerous  to  seize  it,  as,  in  consequence 
of  the  ball's  great  velocity,  the  hand  would  probably  be  injured. 
The  fall  of  bodies,  making  no  allowance  for  the  resistance  of  the 
air  (§  57),  is  an  instance  of  uniformly  accelerated  motion  (§  53). 

Quest.  70.  Is  the  form  of  the  earth  affected  by  its  revolution  on  its  axis  ? 
What  distance  does  the  surface  of  the  earth  move  at  the  equator  in  a  minute 
by  its  rotation  over  its  axis  ?  Is  the  equatorial  or  the  polar  diameter  greatest  ? 
How  is  this  modification  of  the  form  of  the  earth  by  its  rotation  on  its  axis 
illustrated  by  experiment  ?  Why  does  the  form  of  the  brass  hoops  change 
when  made  to  revolve  rapidly  ?  71.  Why  dp  bodies,  when  unsupported,  fall 
towards  the  earth  ?  Is  the  motion  of  a  falling  body  uniform  ?  What  kind 
of  motion  is  the  fall  of  a  heavy  body  an  instance  of? 


40  NATURAL     PHILOSOPHY. 

72.  To  prepare  for  the  discussion  of  this  subject,  let  us  sup- 
pose that  four  men,  with  clubs  in  their  hands,  are  standing  in 
a  row  on  smooth  ice,  and  at  such  a  distance  from  each  other 
that  if  the  first  strikes  a  ball  lying  on  the  ice  before  him,  after 
it  has  been  moving  a  second,  the  second  man  may  give  it  a 
blow  precisely  equal  to  the  first,  and  in  the  same  direction ; 
and  at  the  end  of  another  second,  the  third  may  strike  it  a  third 
blow  just  equal  also  to  the  first,  and  in  the  same  direction ;  and 
at  the  end  of  the  third  second,  the  fourth  man  may  strike  it  in 
like  manner.  We  will  suppose  that  the  ball  suffers  no  resist- 
ance from  the  air  or  from  friction  on  the  ice ;  and  therefore, 
when  an  impulse  is  given  it,  it  moves  on  with  uniform  velocity, 
and  that  the  blow  given  it  by  each  man  would  cause  it  to  move 
sixteen  feet  in  a  second.  The  first  man  standing  at  A,  figure 
30,  would  give  it  an  impulse  that  would  carry  it  sixteen  feet  to 


Fig.  30. 

B,  the  first  second ;  if  it  should  receive  no  impulse  from  the 
second  man  B,  it  would  move  on  just  sixteen  feet  the  next  se- 
cond; but,  receiving  an  additional  impulse  from  B  equal  to 
that  received  from  A,  it  will,  during  the  second  second,  move 
twice  sixteen  or  thirty-two  feet  to  C.  On  arriving  at  C,  its  velo- 
city already  acquired  from  the  impulses  of  A  and  B  would  cause 
it  to  move  thirty-two  feet  during  the  third  second  ;  but,  receiving 
a  third  impulse  from  C  equal  to  each  of  the  others,  it  would, 
during  this  second,  move  three  times  sixteen  or  forty-eight  feet 
to  D.  So,  during  the  fourth  second,  by  receiving  the  impulse 
of  D,,it  would  move  four  times  sixteen  or  sixty-four  feet  to  E. 

73.  Now,  the  circumstances  attending  the  fall  of  bodies  are 
similar  to  the  above,  but  with  this  essential  difference,  that  the 
force  which  puts  them  in  motion,  instead  of  acting  by  successive 
impulses,  acts  constantly.  Let  us  proceed  to  inquire  what  dif- 
ference this  will  produce  in  the  results. 

As  the  force  which  acts  the  first  instant  to  put  the  body  in 
motion  continues  to  act  at  each  successive  instant  with  the 
same  uniform  intensity,  and  of  course  communicates  at  each 
instant  the  same  velocity,  it  is  evident  that  if,  at  the  end  of  any 
given  portion  of  time,  as  a  second,  this  force  (gravitation)  should 
cease  to  act,  the  velocity  already  acquired  would  alone  carry  it 
during  the  next  second  through  twice  the  space  it  moved  through 
during  the  first  second.  But  as  the  force  really  acts  during  the 

Quest.  72.  How  are  the  four  men  on  the  ice  supposed  to  be  arranged  ? 
How  far  is  the  ball  supposed  to  move  the  first  second  by  the  impulse  given 
it  by  the  first  man  ?  How  far  will  it  move  the  next  second  ?  How  far  the 
third,  and  how  far  the  fourth  second?  73.  Does  gravity  act  by  successive 
impulses  ?  As  gravitation  acts  constantly,  communicating  at  each  instant 
the  same  velocity,  if,  at  the  end  of  any  given  time,  as  a  second,  it  should 
cease,  how  much  farther  would  the  body  fall  the  next  second  merely  by  its 


MECHANICS.  41 

second  second,  as  well  as  the  first,  it  will  add  the  same  amount 
to  its  motion  as  it  gave  it  during  the  first  second ;  altogether, 
then,  during  the  second  second,  it  will  fall  through  three  times 
the  space  it  did  during  the  first.  During  the  two  seconds  from 
the  beginning  of  the  motion,  the  body  will  fall  through  four 
times  the  distance  it  fell  the  first  second. 

74.  So,  the  velocity  acquired  at  the  end  of  the  second  second 
will  (if  gravitation  should  cease  to  act)  carry  it  twice  as  far 
during  the  next  two  seconds  as  it  passed  the  first  two ;  that  is, 
its  acquired  velocity  will  cause  it  to  traverse  during  the  third 
and  fourth  second  twice  the  space  it  traversed  during  the  first 
two  seconds,  or  eight  times  the  distance  it  traversed  the  first 
second  alone.  Half  of  this  distance,  or  four  times  the  space 
passed  the  first  second,  of  course  it  will  pass  through  the  third 
second  by  its  acquired  velocity ;  but,  to  find  the  whole  distance 
it  will  really  traverse  the  third  second,  we  must  consider  gravity 
as  acting  and  communicating  the  same  amount  to  its  motion  as 
during  the  first  second.  The  whole  space  passed  over  during 
the  third  second  will  therefore  be  just  five  times  that  passed 
over  during  the  first.  In  the  same  manner  it  might  be  shown 
that  during  the  fourth  second  the  body  will  fall  seven  times  as 
far  as  it  did  the  first,  and  during  the  fifth  second  nine  times  as 
far,  and  so  on,  the  spaces  passed  each  second  from  the  beginning 
of  the  motion  being  as  the  odd  numbers  1,  3,  5,  7,  9,  11,  &c. 

75.  This  may  be  illustrated,  to  some  advantage, 
in  the  following  manner.  When  a  body  moves 
uniformly,  we  determine  the  distance  it  traverses 
in  a  given  time,  as  five  seconds,  by  multiplying 
the  time  by  its  velocity.  Thus,  if  a  body  moves 
twenty  feet  a  second,  it  will  in  five  seconds  tra- 
verse five  times  twenty  or  one  hundred  feet. 

Now  if,  in  figure  31,  we  let  the  line  A  B  represent 
the  velocity  of  the  body  (twenty  feet  per  second), 
and  the  line  A  C  the  time  of  its  motion  (five  se- 
conds), the  surface  of  the  figure  ACD  B,  which  is 
equal  to  A  B  multiplied  by  A  C,  will  represent  the 
space  passed  over  (one  hundred  feet),  in  the  five 
Fig.  31.  seconds.  There  is,  indeed,  no  resemblance  be- 
tween space  passed  over  by  a  moving  body  (which 

acquired  velocity,  than  it  fell  the  first  second?  But  as  gravitation  would 
really  act  during  this  second,  as  well  as  the  first,  how  much  motion  would 
this  add  to  that  acquired  during  the  first  second  ?  Altogether,  then,  how  far 
should  the  body  fall  during  the  second  second  ?  How  far  would  it  fall  during 
the  first  two  seconds  ?  74.  How  far  will  the  body  fall  by  its  acquired  velo- 
city during  the  third  second  ?  How  far  will  it  fall  during  the  third  second 
by  its  velocity  previously  acquired,  and  by  the  action  of  gravity  taken  toge- 
ther ?  How  far  will  it  fall  the  fourth  second  ?  How  far  the  fifth,  and  how 
far  the  sixth  second  ?  75.  When  a  body  moves  uniformly,  how  do  we  de- 
termine the  distance  it  will  traverse  in  a  given  time  ?  How  do  we  determine 
4* 


42 


NATURAL    PHILOSOPHY. 


D 


Fig.  32. 


is  a  line)  and  a  surface;  but  as  the  surface  of  a  rectangle,  as 
A  C  D  B,  is  found  by  multiplying  together  any  two  of  its  adja- 
cent sides ;  and  as  the  space  passed  over  by  a  moving  body,  by 
multiplying  the  time  of  its  motion  by  its  velocity ;  it  is  evident 
that  the  space  passed  over  by  a  moving  body  sustains  the  same 
numerical  relation,  to  the  time  of  its  motion  and  its  velocity,  as 
the  surface  of  a  rectangle  sustains  to  any  two  of  its  adjacent 
sides.  For  numerical  calculations,  therefore,  these  three  latter 
things  respectively  may  be  taken  to  represent  the  three  former. 
A  ^  76.  In  the  above  case  (§  72)  of  the  four 

men  upon  the  ice,  let  A  B,  figure  32,  repre- 
sent the  velocity  communicated  to  the  ball 
by  the  first  man,  and  A  C  the  time  (one 
second)  of  its  motion  before  receiving  its  se- 
cond impulse ;  then  will  the  surface  A  C  D  B 
represent  the  space  (twenty  feet)  traversed 
in  this  time.  The  acquired  velocity  would 
now  of  itself  cause  it  to  move  through  a 
space  equal  to  that  already  traversed,  which 
may  be  represented  by  the  surface  C  E  H  D ; 
but,  letting  D  F  represent  the  velocity  com- 
municated by  the  second  man,  the  distance 
it  will  move  during  the  second  second  will 
be  represented  by  the  whole  surface  C  E  G  F. 
So,  it  will  readily  be  seen,  the  remaining  parts  of  the  figure 
will,  in  like  manner,  represent  the  spaces  passed  over  during 
the  third  and  fourth  seconds. 

77.  But  gravitation,  as  we  have  seen,  acts  constantly  and  not 
by  successive  impulses ;  and  a  falling  body  at  the  end  of  any 
given  time,  as  a  second,  will  have  acquired  sufficient  velocity 
to  carry  it  the  next  second,  if  gravity  ceased  to  act,  twice  as 
far  as  it  fell  the  first  second.  (§  73.) 

Now,  if  we  let  the  line  A  a,  figure  33,  represent  the  time 
of  falling  (one  second)  of  a  falling  body,  and  ab  the  velo- 
city acquired  at  the  end  of  this  time,  then,  as  the  motion  has 

the  surface  of  a  rectangle  when  its  two  adjacent  sides  are  known  ?  How  does 
it  appear  that  the  surface  of  a  rectangle  sustains  the  same  numerical  relation 
to  its  two  adjacent  sides  as  the  space  passed  over  by  a  body  moving  uniformly 
sustains  to  its  velocity  and  the  time  of  its  motion  ?  76.  In  the  case  of  the 
ball  moving  on  smooth  ice  by  four  successive  impulses,  what  part  of  figure 
32  represents  the  space  it  would  move  during  the  first  second  by  the  first 
impulse  ?  What  part  represents  the  space  it  would  pass  the  next  second  by 
its  acquired  motion  ?  What  part  represents  the  whole  space  it  would  pass 
during  this  second  ?  77.  What  part  of  figure  33  represents  the  space  a  body 
will  fall  by  the  force  of  gravity  the  first  second  ?  What  part  represents  the 
space  it  would  pass  the  next  second  by  its  acquired  velocity  only  ?  What 
part  represents  the  space  gravity  alone  would  cause  it  to  pass  during  this  se 
cond  ?  What  part  represents  the  space  it  would  pass  the  second  second  by 
its  velocity  previously  acquired,  and  by  the  continued  action  of  gravity  toge- 
ther ?  What  part  represents  the  spa>ce  it  would  pass  the  third  second  ? 


MECHANICS. 


43 


Fig.  33. 


been  uniformly  accelerated, 
will  the  triangle  Aab  repre- 
sent the  space  passed  over 
during  the  second.  If,  now, 
gravity  should  cease  to  act, 
the  velocity  would  be  uniform ; 
and,  during  the  next  second, 
the  space  traversed  may  be  re- 
presented by  the  square  a  c  d  6, 
which  it  will  be  seen  is  just 
equal  to  twice  the  triangle 
Aab;  but,  in  reality,  during 
this  second,  gravity,  by  its 
continued  action,  would  com- 
municate the  same  motion  as 
it  did  during  the  first,  and  the 


body  would  traverse  the  space  represented  by  the  figure  a  c  e  6, 
which  is  equal  to  three  times  the  triangle  Aab. 

In  the  same  manner  it  might  be  shown  that,  during  the  next 
or  third  second,  it  would  traverse  a  space  represented  by  the 
surface  cfi  e,  which  is  five  times  the  triangle  A  a  b;  and  during 
the  fourth  second  a  space  represented  by  the  surface  fj  m  i, 
which  is  seven  times  A  a  6,  &c. 

78.  If  we  wish  to  determine  the  distance  the  body  will  fall  in 
any  given  time  from  the  beginning  of  the  motion,  we  find  that 
during  the  first  second  it  moves  through  a  certain  space  repre- 
sented by  the  triangle  A  a  b;  during  the  first  two  seconds  it 
moves  through  a  space  represented  by  the  triangle  Ace,  which 
is  four  times  A  a  b;  during  three  seconds,  through  a  space  re- 
presented by  the  triangle  A  fi,  which  is  equal  to  nine  times 
A  a  6,  &c.    The  spaces  passed  over  in  different  times  from  the 
beginning  of  motion,  therefore,  are  as  the  squares  of  the  times ; 
that  is,  in  two  seconds  it  will  fall  twice  two,  or  four  times  as  far 
as  it  fell  the  first  second ;  in  three  seconds,  three  times  three, 
or  nine  times  the  distance  it  fell  the  first,  and  so  on. 

79.  The  law  of  falling  bodies,  as  above  developed,  may  be 
fully  demonstrated  experimentally  by  means  of  Atwood's  ma- 
chine, so  called  from  the  name  of  its  ingenious  inventor;  but  it 
is  too  complex  to  be  here  described. 

80.  Now  it  has  been  found  by  numerous  and  accurate  ob- 
servations that  bodies  falling  freely  by  the  force  of  gravity  pass 

Quest.  78.  What  part  of  the  same  figure  represents  the  space  the  body 
will  fall  during  the  first  two  seconds  ?  During  the  first  three  seconds  ? 
During  four  seconds  ?  What  is  the  ratio  of  the  spaces  passed  over  from  the 
beginning  of  the  motion  as  compared  with  the  times  ?  What  is  the  square 
of  a  number  ?  79.  What  is  the  design  of  Atwood's  machine  ?  80.  How  far 
is  it  found  by  experiment  a  body  falling  freely  will  move  the  first  second  ? 
How  far  will  it  move  the  next  second  ?  How  far  the  third,  and  how  far  the 
fourth  second  ? 


44  NATURAL     PHILOSOPHY. 

through  16FV  feet  the  first  second  of  time;  which,  however,  as 
it  is  sufficiently  accurate  for  our  purpose,  in  order  to  avoid  the 
inconvenience  of  fractions,  we  will  call  16  feet. 

The  spaces  passed  through  during  the  several  seconds,  then, 
will  be  as  follows.  The  body  will  fall  during 

The  1st  second  .  ...................  1  X  16=  16  feet. 

«    2d       "         ....................  3x16=48    " 

"    3d       "         ....................  5x16=80    " 

"    4th      "         ....................  7x16=112    " 

"    5th     "         ....................  9x16=144     "  &c. 

81.  The  spaces  passed  over  from  the  beginning  of  the  motion 
will  be  as  in  the  following  table.  The  body  will  pass  over, 
during 

The  1st  second  .............  (12=  I)xl6=  16  feet. 

"     1st  two  seconds  ........  (22=  4)xl6=  64    " 

"      "three      "         ........  (32=  9)x  16=144    " 

"      "    four      "        ........  (42=16)x  16=256    "  &c. 

That  is,  the  spaces  passed  over,  as  stated  above  (§  78),  are  as 
the  squares  of  the  times;  if  the  body  passes  over  16  feet  the 
first  second,  it  passes  over  22  or  4  times  16  feet  during  the  first 
two  seconds,  and  32  or  9  times  16  feet  in  three  seconds.  Hence, 
to  find  the  distance  a  heavy  body  will  fall  in  a  given  time,  we 
have  the  following  rule,  viz.  Multiply  the  distance  it  will  fall 
in  one  second  (16r^  ft.),  by  the  square  of  the  time  in  seconds. 

Suppose  it  was  required  to  determine  how  far  a  heavy  body 
would  fall  in  8  seconds.    By  the  above  rule,  8  X  8=64,  and  64 
=  10291  feet. 


82.  An  easy  methqd  of  determining  the  depth  of  a  well,  or 
the  height  of  a  tower,  naturally  suggests  itself  here.  Suppose 
a  person  standing  at  the  mouth  of  a  well,  the  depth  of  which  to 
the  surface  of  the  water  he  wishes  to  ascertain.  Having  a 
watch  with  a  second-hand,  he  finds  that  a  lead  bullet  let  fall 
strikes  the  water  in  just  2i  seconds.  Thus,  by  the  rule  given 
above,  2|x2|=6{,  and  6£x  16TV=100  feet,  ||  which  is  the  depth 
required! 

It  is  evident  that  some  little  time  would  be  required  for  the 
sound  of  the  bullet  in  striking  the  water  to  reach  the  ear;  but 
it  would  be  so  trifling  that  it  may  be  entirely  neglected. 

Quest.  81.  How  far  will  the  body  fall  the  first  two  seconds  ?  How  far  in 
three  seconds  ?  What  is  the  rule  for  finding  the  distance  a  heavy  body  will 
fall  in  any  given  number  of  seconds  ?  82.  How  may  we  readily  determine 
the  depth  of  a  well  by  letting  fall  a  heavy  body  into  it  ? 


MECHANICS.!.':  45 

83.  If  a  body  is  projected  downward  with  a  given  velocity, 
the  effect  of  gravitation  is  to  be  calculated  as  above,  and  to 
this  the  distance  it  would  traverse  by  the  projectile  force  is  to 
be  added.  Thus,  if  a  body  be  projected  downward  with  a  velo- 
city of  50  feet  a  second,  at  the  end  of  three  seconds  it  will  have 
fallen  by  the  force  of  gravity  32  or  9x  16=144  feet;  and  to  this 
we  are  to  add  150  feet,  the  distance  it  is  projected,  making  in 
all  294  feet. 

It  is  required  to  determine  how  far  a  body  will  fall  in  7  se- 
conds, which  is  projected  downward  with  a  velocity  of  75  feet 
per  second. 

Answer.  It  would  fall  b.y  the  action  of  gravity  788^  feet,  and 
by  the  force  with  which  it  is  projected  525  feet,  making  toge- 
ther 1313TV  feet. 

84.  If  the  body  is  projected  perpendicularly  upward,  the  dis- 
tance it  will  rise  by  the  force  of  projection  is  to  be  first  calcu- 
lated; and  from  this  the  distance  it  would  fall  in  the  same  time 
by  gravitation  is  to  be  subtracted.  In  the  above  example  (§  83), 
if  we  suppose  the  body  to  have  been  projected  perpendicularly 
upward,  and  suppose  that  for  the  time  gravitation  should  cease 
to  act,  it  would  have  risen  by  the  projectile  force  50  x  3=  150 
feet ;  but,  as  gravitation  acts  constantly,  the  distance  it  would 
fall  in  the  given  time  by  this  force,  or  144  feet,  must  be  sub- 
tracted from  the  150  to  find  the  height  to  which  it  would  really 
ascend,  which  would  be  only  6  feet. 

85.  It  is  impossible,  under  any  circumstances,  to  remove  a 
body  from  the  influence  of  gravity.   When  at  rest,  the  body  by 
this  force  presses  upon  the  substance  which  supports  it ;  if  the 
support  is  removed,  it  falls  with  a  uniformly  accelerated  velocity, 
as  we  have  seen ;  if  it  is  projected  perpendicularly  upward  or 
downward,  the  action  of  gravity  is  to  be  taken  into  account,  to 
find  its  real  motion,  and  subtracted  or  added,  as  the  case  may 
be ;  and  if  it  be  projected  in  any  other  direction,  this  force 
equally  exerts  its  influence.    If  a  body  be  projected  horizontally 
over  a  horizontal  plane,  it  will  strike  the  surface  in  the  same 
time  it  would  if  allowed  to  fall  freely  by  the  force  of  gravity 
alone.    The  only  effect  of  the  projection  has  been  to  cause  it  to 
strike  at  a  distance  from  the  place  to  which,  but  for  this,  it 
would  have  fallen  in  a  straight  line.    This  principle  is  of  great 

Quest.  83.  If  a  body  is  projected  perpendicularly  downward,  how  is  the 
distance  it  will  move  in  a  given  time  to  be  determined  ?  If  a  body  is  project- 
ed downward  with  a  velocity  of  fifty  feet  per  second,  how  far  will  it  move  in 
three  seconds  ?  84.  When  a  body  is  projected  perpendicularly  upward,  how 
will  it  be  affected  by  gravity  ?  How  is  the  distance  it  will  move  in  a  given 
time  to  be  determined  ?  If  a  body  were  projected  upward  with  a  velocity  of 
fifty  feet  per  second,  how  far  would  it  move  in  three  seconds  ?  85.  Is  it  pos- 
sible by  any  means  to  remove  a  body  from  the  influence  of  gravity  ?  When 
a  body  is  at  rest,  how  is  it  influenced  by  this  force  ?  Will  a  body  projected 
horizontally  over  a  horizontal  plane  strike  the  plane  in  the  same  time  as  if  it 


46  NATURAL     PHILOSOPHY. 

importance  in  the  firing  of  cannon ;  and  it  will  be  seen  from 
what  has  been  said  that  it  is  absolutely  impossible  to  fire  a  ball 
in  a  straight  line  except  perpendicularly,  either  upward  or 
downward.  As  soon  as  it  has  left  the  mouth  of  the  cannon  it 
must  begin  to  fall,  if  projected  horizontally ;  or,  if  projected  in  a 
more  elevated  direction,  it  is  prevented  from  rising  as  far  as  it 
otherwise  would,  and  describes  a  curve  called  a  parabola. 

Thus,  if  a  ball  be  fired  in  the  direc- 
tion A  G,  figure  34,  it  will  not  pass 
on  in  the  line  AEG,  but  will  at  once 
begin  to  fall  below  it.  Let  us  suppose 
the  force  of  the  powder  sufficient,  but 
for  the  influence  of  gravity,  to  throw 
the  ball  from  A  to  E  in  one  second  ; 
as  soon  as  it  left  the  gun  it  would 
begin  to  fall  by  the  force  of  gravity 
34>  acting  upon  it,  and  at  the  end  of  the 

second  it  would  be  at  F  instead  of  E, 
and  the  distance  EF  would  be  found  just  16^  feet  (580),  the 
distance  which  a  body  falls  by  the  force  of  gravity  in  a  second 
of  time.  So,  at  the  end  of  two  seconds,  the  ball  would  be  found 
at  H  instead  of  G,  where  the  projectile  force  alone  would  have 
carried  it;  and  the  distance  GH  would  be  equal  to  64i  feet, 
the  space  a  heavy  body  falls  through  in  two  seconds.  The  body, 
therefore,  would  describe  the  curved  line  A  H  B. 

It  is  found  by  experiment  that  the  ball  goes  farthest  when  the 
piece  is  elevated  about  45°,  or  half-way  between  a  horizontal 
and  a  perpendicular  line.  If  the  piece  is  elevated  more  than 
this,  the  ball  rises  higher,  but  strikes  the  ground  nearer,  as  at 
C ;  or,  if  it  is  elevated  less  than  45°,  it  comes  to  the  ground 
sooner,  as  at  D,  though  its  path  is  less  curved. 

86.  If  a  body,  instead  of  falling  perpendicularly,  is  made  to 
roll  freely  down  an  inclined  plane,  the  same  laws  of  acceleration 
of  motion  prevail  with  regard  to  the  motion  along  the  plane, 
but  the  velocity  will  be  less  rapid  in  proportion  as  the  height  of 
the  plane  is  less  than  its  length.  Thus, 
the  motion  of  a  body  gliding  freely  down 
the  inclined  plane,  A  B,  figure  35,  will  be 
uniformly  accelerated,  but  its  velocity 

^  will  be  to  the  velocity  of  a  body  falling 

Fie  35  "  vertically,  as  the  height  of  the  plane  is 

to  its  length,  that  is,  as  A  C  is  to  A  B. 
In  what  has  been  said  of  the  motion  of  bodies,  it  is  of  course 

fell  perpendicularly  ?  Does  the  ball  fired  horizontally  from  a  cannon  proceed 
in  a  straight  line  ?  What  is  the  curve  called  which  the  ball  describes  ?  In 
what  direction  must  the  piece  be  pointed  in  order  that  the  ball  may  proceed 
the  greatest  distance  ?  86.  Is  the  motion  of  a  body  rolling  freely  down  an 
inclined  plane  uniformly  accelerated  ?  Will  it  have  attained  the  same  velo- 
city on  reaching  the  foot  of  the  plane  as  if  it  had  fallen  vertically  through  the 


MECHANICS.  47 

to  be  understood  that  no  allowance  has  been  made  for  the  re- 
sistance of  the  atmosphere  (§  57),  which  in  some  cases  is  very 
great,  and  very  much  modifies  the  final  result.  The  resistance 
of  the  atmosphere  to  a  ball  of  three  pounds  weight,  moving  with 
a  velocity  of  1700  feet  a  second,  is  computed  to  be  equal  to  154 
pounds. 

87.  It  is  to  be  observed  also,  that  the  laws  of  falling  bodies, 
above  developed,  apply  only  to  bodies  falling  within  moderate 
distances  of  the  earth's  surface.    We  have  considered  the  force 
of  gravity  as  absolutely  uniform,  which  is  not  true  in  fact,  ex- 
cept within  comparatively  small  distances  of  the  surface.     We 
have  seen  (§34),  that  above  the  earth's  surface  the  force  of 
gravity  diminishes  as  the  square  of  the  distance  from  the  centre 
increases ;  and  consequently  4000  miles  above  the  earth  it  is 
only  one-fourth  as  great  as  at  the  surface.     If,  then,  we  should 
attempt  to  calculate,  by  our  rule,  the  time  a  body  would  fall 
through  this  distance  to  the  earth,  we  should  not  obtain  an  ac- 
curate result,  because  in  this  distance  the  force  of  gravity  is 
constantly  varying.    A  more  complex  rule  is  required  in  this 
and  similar  cases,  which  it  would  be  out  of  place  here  to  inves- 
tigate. 

88.  As  the  attraction  of  the  earth  diminishes  rapidly  at  great 
distances,  there  is  a  limit  beyond  which  the  velocity  of  a  falling 
body  cannot  increase,  however  great  the  distance  from  which 
it  may  fall.     It  has  been  determined  by  mathematicians  that  a 
body  falling  to  the  earth  from  the  sun  or  from  one  of  the  stars, 
if  it  were  possible,  would  not  attain  on  arriving  at  the  earth  a 
velocity  of  quite  seven  miles  a  second ;  and  more  than  half  of 
this  velocity  would  be  communicated  to  the  body  while  passing 
through  the  last  1400  miles. 

89.  As  the  attraction  between  two  bodies  must  always  be 
mutual  and  equal  (§  60),  it  is  evident  that  when  the  earth  attracts 
a  body,  it  must  itself  also  be  attracted  ;  and  if  the  body  moves 
towards  the  earth,  the  earth  must  also  move  towards  the  other 
body.  As,  however,  any  mass  which  in  its  fall  can  come  under 
the  observation  of  man  must  be  infinitely  small  when  compared 
with  the  earth,  so  the  distance  through  which  the  earth  would 
be  moved  would  be  infinitely  smaller  compared  with  the  dis- 
tance the  body  would  fall. 

height  of  the  plane  ?  Will  the  time  of  its  falling  be  increased  or  diminished  ? 
Is  any  allowance  here  made  for  the  resistance  of  the  air  ?  What  does  the  re- 
sistance of  the  air  amount  to  on  a  ball  of  three  pounds  weight  moving  1700 
feet  a  second  ?  87.  Do  these  laws  of  falling  bodies  apply  to  bodies  falling 
at  great  distances  from  the  earth's  surface  ?  How  much  is  the  earth's  attrac; 
tion  diminished  4000  miles  from  the  surface  ?  88.  What  is  the  greatest  velo- 
city a  body  can  attain  in  falling  from  the  greatest  distances  to  the  earth  ? 
89.  Is  the  earth  attracted  by  falling  bodies  ?  Why  is  not  its  motion  percep- 
tible ? 


48  NATURAL     PHILOSOPHY. 

90.  The  mean  distance  of  the  moon  from  the  earth's  centre 
is,  as  we  have  seen  (§  35),  about  60  times  the  semi-diameter  of 
the  earth.  This  is  found  by  dividing  240000  miles,  which  is  the 
mean  distance  of  the  moon,  by  4000,  which  is  very  nearly  the 
earth's  semi-diameter  or  radius.    Consequently,  the  earth's  at- 
traction at  the  moon  will  be  only  ^^th  as  great  as  it  is  at  the 
surface;  and  a  body  during  the  first  second  or  minute  will  fall 
only  sa^th  as  far  as  it  would  in  the  same  time  if  let  fall  near 
the  earth. 

91.  Now,  by  the  rule  above  given  (§81),  it  is  easily  determined 
that  a  body  falling  unobstructed  near  the  earth  would  in  one 
minute  pass  through  57900  feet,  and  g^th  of  this  is  16 ^  feet- 
That  is,  a  body  at  the  distance  of  the  moon  would  fall  towards 
the  earth  just  the  same  distance  in  a  minute,  as  it  would  fall  if 
near  its  surface  in  a  second. 

92.  As  the  moon  revolves  round  the  earth  in  an  orbit  very 
nearly  circular,  it  is  of  course  acted  on  by  two  forces,  the  centri- 
petal and  the  centrifugal  (§  66) ;  by  the  former  of  which  it  is  con- 
stantly drawn  towards  the  earth,  while  by  the  latter  it  tends  to 
fly  off  into  space.  If  either  of  these  was  destroyed,  it  would  of 
course  obey  the  other  exclusively. 

93.  Now,  it  is  not  difficult  to  show  that  the  moon  does  vir- 
tually fall  towards  the  earth  16yV  feet  every  minute;  or,  in  other 
words,  that,  if  its  centrifugal  force  were  destroyed,  it  would  at 
once  fall  towards  the  earth  with  a  velocity  that  would  cause  it 
to  pass  over  this  distance  the  first  minute  of  time.   That  is,  the 
moon,  if  left  to  the  influence  of  its  centripetal  force  alone,  would 
approach  the  earth  in  one  minute  through  precisely  the  same 
space  that  a  heavy  body  would  fall  by  the  law  of  gravitation 
if  placed  at  that  distance  from  the  earth.  From  this  it  of  course 
follows  that  the  moon's  centripetal  force  is  nothing  but  the 
earth's  attraction  acting  upon  it  as  it  would  upon  any  other 
mass  of  matter  placed  at  the  same  distance. 

Let  E,  figure  36,  be  the  earth,  and  M  N  L  the  moon's  orbit. 
The  moon  revolves  around  the  earth  in  27  days,  7  hours,  and 
43  minutes,  or  39343  minutes,  and  in  one  minute  passes  over 
7^__  part  of  its  orbit,  or  about  33  seconds  of  a  degree.  Let 
M  N  be  this  arc.  By  the  centrifugal  force  alone,  it  would,  in 
one  minute,  describe  the  straight  line  M  O  ($  67),  while,  by  the 

Quest.  90.  How  many  times  the  earth's  semi-diameter  is  the  moon  distant 
from  the  earth  ?  How  is  this  found  ?  How  great  is  the  earth's  attraction  at 
the  distance  of  the  moon  ?  91.  How  far  will  a  body  fall  in  a  minute  near  the 
earth?  How  far  in  a  minute  at  the  distance  of  the  moon  ?  92.  If  the  moon's 
centrifugal  force  were  destroyed,  what  would  be  the  effect  upon  her  ?  93.  Does 
the  moon  virtually  fall  towards  the  earth  16J-  feet  every  minute  ?  What 
follows  from  this  ?  What  is  the  explanation  of  figure  36  ? 


MECHANICS 


49 


centripetal  force  alone,  it  would 
move  from  M  to  P.  But  the 
line  M  P  is  called  the  versed 
sine  of  the  arc  M  N,  which  in 
this  case  is  33";  and  the  versed 
sine  of  an  arc  of  33",  in  a  circle 
whose  radius  is  240000  miles, 
is  found  to  be  16rV  feet  very 
nearly. 

94.  This  is  substantially  the 
celebrated  calculation  of  New- 
ton in  confirmation  of  the  law 
of  universal  gravitation,  which 
was  first  suggested  by  him. 
As  he  drew  near  the  close  of  it, 
and  perceived  the  result  would 
F'?- 36-  be  as  he  anticipated,  conscious 

of  its  momentous  importance,  it  is  said  he  was  so  affected  that 
he  was  unable  to  proceed,  and  was  obliged  to  call  in  an  assistant 
to  complete  it.  (See  Brews ter^s  Life  of  Newton,  Harper's  Family 
Library,  vol.  xxvi.  p.  144.) 


COLLISION    OF     BODIES. 

95.  The  force  with  which  a  moving  body  strikes  another  at 
rest  is  called  its  momentum,  and  is  found  by  multiplying  its  weight 
by  its  velocity.     When  the  weight  of  two  bodies  is  equal,  their 
momenta  will  be  in  proportion  to  their  velocities ;  and  if  the 
velocity  of  two  bodies  is  equal,  their  momenta,  or  quantity  of 
motion,  will  be  in  proportion  to  their  weights.  The  momentum 
of  a  body  is  found,  therefore,  by  multiplying  its  weight  by  its 
velocity.     If  the  weight  is  5,  and  its  velocity  20,  its  momentum 
will  be  20x5=100. 

A  light  body,  therefore,  by  having  its  velocity  increased,  may 
be  made  to  strike  an  obstacle  with  as  much  force  as  a  heavier 
one  which  moves  more  slowly.  A  cannon-ball,  of  3  pounds 
weight,  moving  with  a  velocity  of  900  feet  a  second,  will  possess 
the  same  momentum,  and  strike  a  body  at  rest  with  the  same 
force  as  another  of  90  pounds  weight,  moving  at  the  rate  of  30 
feet  only  per  second ;  for  900x3=2700,  and  90x30=2700. 

96.  The  term  percussion,  or  collision,  is  sometimes  used  to 
indicate  the. force  with  which  a  moving  body  strikes  another; 

Quest.  94.  What  is  said  to  have  been  the  effect  upon  Newton  when  first 
making  this  calculation  ?  95.  What  is  the  momentum  of  a  body  ?  How  is 
the  momentum  of  a  body  found  ?  How  may  a  light  body  be  made  to  strike 
an  obstacle  with  the  same  force  as  another  which  is  much  heavier  ?  96.  What 
is  meant  by  the  percussion  or  collision  of  bodies  ?  Upon  what  particular  cir- 
cumstance will  the  result  of  the  collision  of  two  bodies  depend  ? 


50  NATURAL     PHILOSOPHY. 

the  meaning  is  the  same  as  momentum.  Sometimes  both  of  the 
bodies  supposed  to  come  in  collision  are  in  motion,  and  at 
others  one  of  them  is  at  rest;  and  when  one  of  the  bodies  is  at 
rest,  it  may  be  movable  or  it  may  be  fixed.  In  all  these  cases 
the  result  will  depend  upon  various  circumstances,  but  espe- 
cially upon  the  elasticity  of  the  bodies. 

97.  In  examining  the  effects  of  the  collision  of  bodies,  it  will 
be  sufficient  to  consider  them  either  as  perfectly  elastic,  or  per- 
fectly inelastic.    When  an  inelastic  body  strikes  perpendicularly 
against  an  immovable  object  with  a  plane  surface,  its  motion 
is  instantly  completely  destroyed  ;  but  if  it  had  been  elastic,  on 
striking  perpendicularly  against  the  fixed  plane,  it  would  have 
rebounded  perpendicularly  without  any  diminution  of  its  velo- 
city, as  we  have  seen  above  ($  62). 

98.  If  two  equal  inelastic  bodies,  moving  with  equal  velocities 
in  opposite  directions,  strike  against  each  other,  the  motion  of 
both  will  be  instantly  destroyed,  and  both  come  to  a  state  of 
rest ;  but,  if  two  equal  elastic  bodies,  moving  in  like  manner, 
strike  against  each  other,  they  will  both  rebound  with  the  same 
velocity  they  possessed  before  coming  in  contact. 

99.  The  rebounding  of  elastic  bodies  is  occasioned  (\  23)  by 
the  particles  at  first  yielding  at  the  point  of  contact,  and  then 
instantly  returning,  with  the  same  force  by  which  they  were 
compressed,  to  their  original  position.   If  the  particles  of  a  body 
are  perfectly  fixed  and  unyielding,  or  if  when  compressed  they 
retain  perfectly  the  position  to  which  they  have  been  forced,  it 
will  be  inelastic. 

100.  If  we  suppose  an  inelastic  body,  A,  at  rest,  to  be  struck 
by  another,  B,  of  equal  weight,  both  will  move  forward  toge- 
ther after  the  collision,  but  with  only  half  the  velocity  which  B 
had  before  the  collision.    Half  the  motion  of  B  would  be  com- 
municated to  A,  and  both  together  would  have  the  same  mo- 
mentum B  had  at  first.     If  B  had  been  twice  as  heavy  as  A,  it 
would  have  lost  by  collision  with  A  only  one-third  of  its  mo- 
tion, and  both  would  have  moved  on  together  with  two-thirds 
of  the  velocity  of  B. 

If  both  bodies  be  supposed  to  be  equal,  and  moving  in  the 
same  direction,  but  B  with  twice  the  velocity  of  A,  B  will  of 
course  overtake  A,  and  will  communicate  one-quarter  of  its  ve- 


Quest.  97.  In  examining  the  results  of  the  collision  of  bodies,  how  may 
we  regard  them  ?  When  an  inelastic  body  strikes  against  an  immovable 
object  with  a  plane  surface,  what  is  the  result  ?  What  is  the  result  when  a 
perfectly  elastic  body  strikes  perpendicularly  against  an  immoveable  solid 
plane?  98.  What  is  the  effect  when  two  equal  inelastic  bodies,  moving  with 
equal  velocities  in  opposite  directions,  come  in  collision  ?  What  would  be 
the  effect  if  the  bodies  were  elastic  ?  99.  What  occasions  the  rebounding 
of  elastic  bodies  ?  What  is  the  condition  of  the  particles  of  inelastic  bodies  ? 
100.  If  an  inelastic  body,  B,  strike  another,  A,  at  rest,  equal  in  weight  to 
itself,  how  would  the  two  move  f  If  B  were  twice  as  heavy  as  A,  how  would 


MECHANICS.  51 

locity  to  A,  which  wil]  therefore  have  its  own  motion  increased 
by  one-half;  and  both  bodies  will  move  on  together  with  three- 
fourths  of  the  original  velocity  of  B,  or  once  and  a  half  that  of 
A.  Thus,  in  every  case  of  collision  between  inelastic  bodies, 
if  one  is  at  rest,  or  both  moving  in  the  same  direction,  the  sum 
of  their  momenta  will  be  the  same  both  before  and  after  colli- 
sion. But  if  they  are  moving  in  opposite  directions,  the  body 
having  the  least  momentum  will  have  its  motion  destroyed, 
while  the  other  will  continue  its  motion  with  a  momentum  equal 
to  the  excess  of  its  original  momentum  over  that  of  the  first. 

101.  But  if  an  elastic  body,  B,  is  made  to  strike  another,  A, 
of  equal  weight  with  itself,  the  motion  of  B  will  be  wholly  com- 
municated to  A,  which  will  move  on  with  the  same  velocity 
before  possessed  by  B.     If  both  bodies  are  in  motion  in  the 
same  direction,  but  B  with  double  the  velocity  of  A,  when  B 
overtakes  A,  they  will  not  move  on  together,  as  would  be  tho 
case  with  inelastic  bodies  (§  100) ;  but  B  will  communicate  to  A 
one-half  of  its  velocity,  by  which  A's  velocity  will  of  course  be 
doubled.    Both  bodies  will  therefore  move  onward  in  the  same 
direction  as  before,  but  'they  will  have  exchanged  velocities, 
A's  velocity  being  now  double  that  of  B's. 

It  will  be  seen,  therefore,  than  when  collision  takes  place  be- 
tween elastic  bodies,  the  velocity  lost  by  the  striking  body, 
and  that  gained  by  the  body  struck,  will  be  twice  as  great  as 
if  the  bodies  were  inelastic. 

102.  These  principles  may  be  very  satisfactorily  illustrated 
by  means  of  balls  suspended  by  small  cords. 

__,      Thus,  let  A  and  B,  figure  37,  be  two 

small  balls  of  soft  putty,  which  is  per- 
fectly inelastic,  suspended  by  cords;  on 
raising  B  a  short  distance  to  the  right, 
and  letting  it  fall  against  A,  keeping  the 
cord  all  the  time  fully  extended,  both 
balls  will  be  found  to  move  together  to 
the  left,  as  to  A'  F ;  but  they  will  move 
to  the  left  of  their  first  position  only 
about  half  as  far  as  B  was  raised  from 
this  position  to  the  right.  The  ball,  B, 
first  falls  by  the  force  of  gravity,  which, 
however,  carries  it  only  to  the  point 

the  bodies  move  after  collision?  In  all  cases  of  the  collision  of  inelastic 
bodies,  provided  they  are  nor  moving  in  opposite  directions,  how  will  the 
sum  of  their  momenta  before  and  after  collision  compare  ?  If  they  are 
moving  in  opposite  directions,  what  will  be  the  result?  101.  If  an  elastic 
body  strikes  another  equal  to  itself  at  rest,  what  is  the  result  ?  When  col- 
lision takes  place  between  elastic  bodies,  how  much  greater  is  the  velocity 
lost  by  the  striking  body  and  that  gained  by  the  body  struck  than  if  the 
bodies  were  inelastic?  102.  How  may  the  collision  of  inelastic  bodies  be 
illustrated  experimentally  by  means  of  balls  of  soft  putty  ? 


52  NATURAL     PHILOSOPHY. 

where  the  cord  by  which  it  is  suspended  becomes  perpendicu- 
lar, and  it  strikes  against  A ;  beyond  this  point  the  action  of 
gravity  is  to  retard  it,  as  well  as  A,  which  will  now  be  put  in 
motion  by  B.  We  see,  therefore,  the  reason  why  they  should 
move  together  after  collision  only  half  as  far  as  B  moved  be- 
fore collision. 

, ,        103.  To  illustrate  the  effect  of  the 

collision  of  elastic  bodies,  let  A  and  B, 
figure  38,  be  two  balls  of  ivory,  which 
is  a  very  elastic  substance,  suspended 
by  cords,  so  as  to  move  freely.  When 
they  have  come  to  a  state  of  rest,  let  B 
be  drawn  aside  a  little  to  the  right,  so 
as  on  falling  to  strike  against  A ;  the 
result  will  be  that  B,  on  striking  A,  will 
communicate  to  it  all  its  motion  (§  101), 
and  A  will  move  on  the  same  distance 
to  the  left  of  its  position  or  rest,  as  B 
was  carried  to  the  right.  On  A's  return 
it  will  strike  in  a  similar  manner  against  B,  which  will  now 
move  to  the  right,  while  A  will  remain  at  rest  until  B  again  re- 
turns, when  the  same  effect  will  be  produced  as  before.  Thus 
the  motion  would  continue  perpetually,  but  for  the  resistance 
of  the  air,  friction  of  the  cord,  &c.,  which  will  eventually  bring 
both  balls  to  a  state  of  rest. 

104.  When  several  elastic  balls  are  suspended  so  as  to  rest 
in  contact  with  each  other,  the  motion  of  the  first  will  be  com- 
municated through  those  at  rest,  and  the  extreme  balls  only 
will  move. 

Let  ABCDEFG, 
figure  39,  be  several 
balls  of  ivory  accurate- 
ly suspended  from  the 
bar  LM  by  cords,  so 
that  the  centres  of  all 
shall  be  in  the  same 

/  \        straight  line.    If  we  re- 

.-/  >^    move  the  extreme  one, 

\J        /'^YVYYYY'S          _     G,  a   distance    to    the 

right,  as  to  G',  and  then 
let  it  fall,  it  will  strike 
against  F  with  a  mo- 
mentum proportional  to 
its  velocity,  but  without  perceptibly  moving  it  or  any  of  the 
intermediate  balls ;  but  A  at  the  other  extreme  will  start  up  to 


•' 

\ 

\ 

'  < 

A.   B    C    I>    S 

Fig.  39. 


Quest.  103.  What  will  be  the  effect  if  balls  of  some  elastic  substance,  as 
ivory,  are  used?  104.  What  will  be  the  effect  if  a  number  of  ivory  balls 
are  used  suspended  side  by  side,  so  as  to  be  in  contact,  and  one  of  the  ex- 


MECHANICS.  53 

A',  a  height  nearly  equal  to  that  to  which  G  had  been  raised. 
This  ball  then  falling  back,  will  strike  against  B,  and  motion 
will  again  be  communicated  to  G,  which  will  move  as  before ; 
and  thus  a  vibrating  motion  will  be  continued  in  the  extreme 
balls,  until,  by  friction  and  other  resistance,  they  are  at  length 
brought  to  a  state  of  rest.  This  curious  action  of  the  balls  is 
occasioned  by  their  almost  perfect  elasticity,  by  which  the  mo- 
tion is  communicated  from  particle  to  particle  of  each  ball, 
almost  without  any  motion  of  the  mass  of  the  ball.  But  as  they 
are  not  in  fact  perfectly  elastic,  all  the  balls,  usually  after  a  little 
time,  acquire  a  slight  vibratory  motion.  This  last  effect  is 
seen  best  when  only  three  balls  are  used. 

If,  in  the  above  experiment,  two  balls  are  drawn  aside  and 
let  fall,  then  the  two  opposite  ones  will  be  thrown  off;  and  so 
of  any  other  number  within  moderate  limits. 

THE     PEND  ULUM. 

105.  The  pendulum  consists  of  a  single  weight  suspended  by 
a  cord  or  rod,  so  as  to  swing  freely.  If  a  rod  is  used,  it  must 
be  flexible  at  the  upper  part,  or  so  suspended  as  to  allow  it  to 
move  freely  backward  and  forward. 

When  a  weight  so  suspended  is  drawn  aside  a  little  from  its 
position  of  rest,  and  then  let  fall,  by  the  action  of  gravity  ($  70) 
it  is  immediately  carried  to  its  first  position  again ;  but  when  it 
arrives  there,  it  has  acquired  considerable  momentum,  which, 
if  there  was  no  resistance  from  the  air  or  other  cause,  would 
be  sufficient  to  carry  it  as  far  to  the  opposite  side  of  the  per- 
pendicular. It  would  then  return  again  by  the  force  of  gravity 
to  the  perpendicular,  and,  by  its  acquired  momentum,  to  the 
position  from  which  it  started,  to  again  commence  its  motion 
precisely  as  before,  and  so  on  for  ever.  But,  in  reality,  a  body 
made  to  vibrate  in  this  manner  soon  comes  to  a  state  of  rest, 
in  consequence  of  the  resistance  of  the  air  and  the  slight  fric- 
tion occasioned  at  the  point  of  suspension. 

Let  C,  figure  40.  be  a  ball  of  some 
heavy  substance  suspended  by  a 
thread.  If  it  be  now  raised  by  the 
hand  to  B  and  let  fall,  it  will  imme- 
diately return  with  a  uniformly  ac- 
celerated motion  to  C,  since  the  law 
governing  the  descent  of  bodies  in 
curved  lines  is  the  same  as  if  they 
descend  perpendicularly  or  down  an 
inclined  plane  (§86).  As  the  body 
passes  beyond  C  by  its  momentum, 

treme  ones  is  drawn  a  little  aside  and  let  fall  against  the  ball  next  to  it? 
Why  do  all  the  balls,  after  a  little  time,  usually  acquire  a  slight  vibratory 
motion  ?  If  two  balls  are  drawn  aside  and  let  fall  against  the  others,  what 
is  the  result  ?  105.  What  is  a  pendulum  ?  What  force  causes  the  motion 


54  NATURAL     PHILOSOPHY. 

the  force  of  gravity  will  act  against  its  motion  with  precisely 
the  same  intensity  as  it  had  before  acted  in  favour  of  it  (5  85) ; 
and,  making  no  allowance  for  the  resistance  of  the  air  or  fric- 
tion, the  body  should  of  course  move  to  A,  making  A  C  pre- 
cisely equal  to  C  B.  From  A  it  will  return  by  the  force  of 
gravity  to  C,  and  the  momentum  thus  generated  will  carry  it 
onward  to  B.  Having  arrived  at  B,  it  will  again  immediately 
return  to  C  and  A  as  before. 

106.  The  motion  of  a  pendulum,  from  its  extreme  point  B  on 
one  side,  to  the  opposite  side  A,  is  termed  an  oscillation  or  vibra- 
tion; and  it  is  a  most  important  circumstance  that,  for  pendu- 
lums of  the  same  length,  all  the  oscillations  are  performed  in 
equal  or  very  nearly  equal  times.    If  the  arcs  through  which  the 
weight  swings  are  very  small,  though  not  perfectly  equal,  the 
oscillations  are  performed  in  precisely  the  same  time ;  but  if  the 
arcs  are  larger,  it  is  found  the  times  required  are  a  little  longer. 

107.  The  duration  of  an  oscillation  does  not,  therefore,  de- 
pend in  the  least  upon  the  nature  of  the  substance  of  which  the 
pendulum  is  made,  nor  upon  the  size  of  the  weight  used. 

108.  As  the  movements  of  the  pendulum  depend  upon  gra- 
vity, this  instrument  affords  an  excellent  mode  of  determining 
the  intensity  of  this  force  at  different  places  on  the  earth's  sur- 
face.    A  pendulum  that  vibrates  3600  times  an  hour  at  the  equa- 
tor, it  is  found  would  vibrate  3613  times  an  hour  at  the  poles, 
which  shows  the  force  of  gravity  to  be  considerably  greater 
at  the  latter  place.     This  is  occasioned  by  the  enlargement  of 
the  earth  at  the  equator,  and  flattening  at  the  poles,  as  already 
illustrated  (§  70),  by  which  the  surface  at  the  poles  is  brought 
nearer  to  the  centre  than  the  surface  at  the  equator.     The  in- 
tensity of  gravity  at  the  poles  is  greater  than  at  the  equator, 
because  the  distance  to  the  centre  of  the  earth  is  less,  the  point 
from  which  gravity  may  be  supposed  to  act  (§  26).    The  action 
of  gravity  is,  indeed,  the  action  of  the  whole  mass  of  the  earth, 
but  the  effect  is  the  same  as  if  it  was  exerted  only  from  the 
central  point.     So  a  pendulum  that  performs  3600  oscilaltions 
per  hour  at  the  surface  of  the  sea,  when  taken  to  the  top  of  a 
neighbouring  mountain  3,37  miles  high,  vibrates  only  3597  times 
an  hour. 

109.  The  times  required  for  pendulums  of  different  lengths 

of  the  pendulum  ?  Why  should  the  distance  it  swings  on  each  side  of  the 
perpendicular  be  equal  ?  106.  What  is  meant  by  an  oscillation  or  vibration? 
107.  Do  the  times  required  for  the  oscillation  depend  upon  the  weight  of  the 
pendulum,  or  the  substance  it  is  composed  of?  108.  Will  a  pendulum  vibrate 
as  rapidly  at  the  equator  as  at  the  poles  ?  What  occasions  the  difference  ? 
Why  may  the  attraction  of  the  earth  be  considered  as  acting  only  from  the 
centre  ?  Will  the  pendulum  vibrate  most  rapidly  at  the  surface  of  the  sea 
or  at  the  top  of  a  mountain  ?  109.  What  is  the  length  of  a  pendulum  that 
vibrates  once  a  second  at  New  York  ?  What  is  the  length  when  it  vibrates 
half  seconds  ? 


MECHANICS.  55 

to  vibrate  are  as  the  square  roots  of  their  length.  Thus,  at  New 
York,  the  pendulum  which  vibrates  seconds  is  found  to  be 
39.1  inches  in  length,  while  that  which  vibrates  half  seconds 
is  only  9.7  inches  long.  Thus,  as  1  :  ^  : :  \/393  :  V&f.  It  may 
easily  be  determined  that  a  pendulum  to  perform  its  oscillations 
in  2  seconds,  must  be  13  feet  in  length. 

110.  A  clock  is  merely  a  machine  propelled  usually  by  a 
weight,  for  the  purpose  of  continuing  the  motion  of  a  pendulum 
and  registering  the  number  of  its  oscillations.     This  last  office 
is   performed   by  the  pointers,   of  which  there  are  usually 
three ;  one  for  seconds,  one  for  minutes,  and  one  for  hours. 
Generally  the  pendulum  of  a  clock  is  made  of  the  proper 
length  to  perform  its  oscillations  either  in  a  half  second  or 
in  a  second  (§  109),  and  the  wheel-work  is  adapted  accordingly. 
When  a  seconds  pendulum  is  used,  it  makes  of  course  60  oscil- 
lations in  a  minute,  3600  in  an  hour,  and  86400  in  24  hours.    A 
person  looking  at  a  clock  in  the  afternoon  observes  that  it  is 
24  minutes  and  35  seconds  past  3,  which  is  in  reality  only  say- 
ing that  since  12  o'clock,  the  point  of  time  at  which  the  reckon- 
ing it  is  supposed  was  commenced,  the  pendulum  has  made 
12275  oscillations  or  beats. 

111.  The  motion  of  a  clock  is  regulated  entirely  by  the  length 
of  the  pendulum ;  and  usually  the  weight  at  its  lower  extremity 
is  sustained  by  a  screw,  by  which  it  may  be  raised  or  lowered 
a  little  at  pleasure. 

But  we  have  seen  (§  106),  that  the  pendulum,  if  left  to  itself, 
by  reason  of  the  resistance  of  the  air  and  the  friction  at  its 
point  of  suspension,  will,  after  a  time,  come  to  a  state  of  rest. 
To  counteract  this  tendency,  the  machinery  of  the  clock  is  so 
constructed,  that,  at  each  oscillation,  it  shall  receive  a  slight 
impulse  from  the  propelling  power,  by  which  means  its  motion 
is  continued  for  any  length  of  time  without  variation. 

112.  Any  change  in  the  length  of  the  pendulum  of  a  clock, 
therefore,  will  seriously  affect  its  going.    Now  this  change  is 
produced  by  change  of  temperature,  the  length  being  increased 
in  warm  weather,  and  diminished  in  cold  weather;  so  that  the 
same  clock  is  usually  found  to  go  faster  in  winter  than  in  sum- 
mer. An  obvious  remedy  is  to  move  the  weight  at  its  extremity 
a  little  up  or  down  as  occasion  may  require.     But  to  do  this 
accurately  would  be  extremely  inconvenient,  not  to  say  im- 
possible,  in   practice;   and   several   contrivances  have   been 
adopted  to  overcome  the  difficulty,  the  most  important  of 

Quest.  110.  What  is  a  clock?  How  does  a  clock  show  the  number  of 
oscillations  the  pendulum  has  made  ?  When  a  person  says  it  is  24  minutes 
and  35  seconds  past  3  in  the  afternoon,  what  may  he  be  understood  to  mean  ? 
111.  How  is  the  motion  of  a  clock  regulated  ?  How  is  the  pendulum  of  a 
clock  kept  in  motion?  112.  Why  do  clocks  generally  go  faster  in  winter 
than  in  summer  ?  What  is  the  object  of  the  gridiron  pendulum  ? 


56 


NATURAL    PHILOSOPHY. 


which  is  the  gridiron  pendulum.  This  is  so  constructed  of 
rods  of  different  metals,  that  the  expansion  or  contraction  of 
the  rods  of  one  metal  in  one  direction,  shall  be  counteracted  by 
an  equal  expansion  or  contraction  of  the  other  in  the  opposite 
direction.  The  two  metals  used  may  be  steel  and  copper,  the 
latter  of  which  is  expanded  or  contracted  by  a  given  change 
of  temperature  much  more  than  the  former. 

In  figure  41,  ABC  D  is  a  parallelogram  of  steel 
fixed  to  the  rod  E,  while  the  bars  F  H  and  G I  are 
of  copper,  and  inserted  firmly  in  the  steel  bar  C  D. 
The  weight,  W,  is  then  attached  to  a.  wire  which 
passes  freely  through  a  hole  in  the  centre  of  C  D, 
and  is  fixed  firmly  in  the  part  FG.  Now  suppose  the 
temperature  to  rise,  the  bars  AC  and  BD  would 
be  expanded,  and  the  length  of  the  pendulum, 
that  is,  the  distance  between  the  points  E  and  W, 
would  be  increased ;  but  the  same  rise  of  tem- 
perature causes  an  expansion  also  of  the  copper 
bars  F  H  and  G  I,  by  which  the  weight  W  will  be 
3  drawn  up,  or  this  distance  between  the  points  E 
and  W  will  be  diminished.  Now,  as  the  lengths 
respectively  of  these  bars  of  copper  and  steel  are 
made  inversely  proportional  to  their  expansibilities 
by  heat,  it  follows  that  the  length  of  the  pendulum, 
Fig.  41.  as  a  whole,  is  preserved  the  same  through  every 
ordinary  change  of  temperature ;  that  is,  the  whole  amount  of 
the  contraction  or  expansion  of  the  steel  part  of  the  pendulum 
is  just  equal  to  the  whole  amount  of  the  contraction  or  expan- 
sion of  the  copper  part ;  and  as  these  changes  of  length  of  the 
two  parts  are  in  opposite  directions,  they  just  balance  each 
other,  and  the  length  of  the  whole  pendulum,  by  which  we 
mean  the  distance  from  the  point  of  suspension  E  to  the  weight 
W,  remains  unchanged. 

The  importance  of  such  an  arrangement  is  obvious  from 
the  fact  that  a  change  of  temperature  of  30°  will  cause  a  varia- 
tion of  about  8  seconds  in  24  hours  in  a  common  clock  with  an 
iron  pendulum.  If  the  pendulum  is  brass  or  copper,  the  varia- 
tion will  be  still  greater.  Sometimes  pendulum  rods  are  made 
of  wood,  which  is  supposed*  to  be  less  affected  by  changes  of 
temperature  than  the  metals. 

MECHANICAL    POWERS. 

113.  The  mechanical  powers  are  simple  machines  or  instru- 
ments, with  which  we  are  accustomed  to  raise  weights  and 
overcome  resistances.  They  are  six  in  number,  viz.  the  Lever, 
the  Wheel  and  Axle,  the  Pulley,  the  Inclined  Plane,  the  Wedge, 


Quest.  113.  What  are  the  mechanical  powers?    How  many  of  them  are 
there  ?    Does  each  one  of  these  act  on  a  distinct  principle  ? 


MECHANICS.  51 

and  the  Screw.  But  as  the  wheel  and  axle  act  essentially  on 
the  same  principle  as  the  lever,  and  the  wedge  and  the  screw 
on  the  same  principle  as  the  inclined  plane,  many  writers  are 
disposed  to  reduce  the  number  of  the  mechanical  powers  to 
three,  viz.  the  lever,  the  pulley,  and  the  inclined  plane. 

114.  All  the  machines,  however  complicated,  which  the  inge- 
nuity of  man  has  ever  invented,  are  nothing  more  than  combi- 
nations of  these  simple  powers.     Though  great  advantage  is 
gained  by  the  use  of  machines,  there  is  no  such  thing,  pro- 
perly speaking,  as  the  creation  of  power  by  them,  as  some 
have  supposed  ;  their  design  seems  to  be  to  exchange  time  for 
power,  as  will  appear  more  fully  hereafter. 

In  the  use  of  any  machine,  whether  simple  or  complex,  three 
things  are  to  be  particularly  considered.  1.  The  force  or  re- 
sistance which  is  to  be  sustained  or  overcome,  which  we  will 
call  the  weight.  2.  The  force  which  is  used  to  produce  the 
effect  desired,  called  the  power.  3.  The  mode  in  which,  by  the 
action  of  the  machine,  the  power  produces  the  proper  effect 
upon  the  weight. 

115.  The  Lever.  —  The  lever  is  an  inflexible  rod  of  metal  or 
other  solid  substance,  capable  of  moving  upon  a  point  of  sup- 
port called  the  fulcrum.   In  what  we  have  to  say  of  it,  no  notice 
will  be  taken  of  its  own  weight. 

There  are  three  kinds  of  lever,  or  rather  three  varieties  of  it, 
depending  upon  the  position  of  the  fulcrum  with  reference  to 
the  power,  or  force  applied  to  move  it,  and  the  weight,  or  re- 
sistance to  be  overcome. 

116.  In  the  lever  of  the  first 

iL  A  5L      kind,  the  power  is  supposed  to 

Oj  4p          liiw  De  applied  at  one  extremity, 

p  and  the  weight  at  the  other, 

Fig.  42.  with  the  fulcrum,  or  point  of 

support  between  them,  as  in 

figure  42,  where  P  is  the  power,  F  the  fulcrum,  and  W  the 
weight.  If  the  fulcrum  is  placed  at  the  centre,  it  is  evident  no- 
thing is  gained,  as  the  power  and  weight  must  be  exactly  equal 
in  order  that  they  may  balance  each  other;  but  when  the  ful- 
crum divides  the  lever  into  two  unequal  arms,  having  the  weight 
upon  the  shorter,  then  the  power  will  be  to  the  weight  as  the 
length  of  the  short  arm  is  to  that  of  the  long  arm.  Thus,  if  in 

Quest.  1 14.  Are  all  machines  merely  combinations  of  those  simple  powers  ? 
Do  they  create  power?  What,  then,  is  their  design?  What  three  things 
are  to  be  considered  in  the  use  of  machines  ?  115.  What  is  the  lever  ?  How 
many  kinds  or  varieties  of  the  lever  are  there  ?  116.  In  the  lever  of  the  first 
kind,  how  are  the  power,  weight  and  fulcrum  situated  with  respect  to  each 
other  ?  If  the  fulcrum  is  in  the  centre,  how  must  the  power  and  weight 
compare  with  each  other  to  produce  an  equilibrium  ?  What  is  the  ratio  of 
the  power  to  the  weight,  when  the  weight  is  attached  to  the  short  arm,  and 
the  power  to  the  long  arm  ?  How  is  figure  42  explained  ?  When  motion  ia 


58 


NATURAL     PHILOSOPHY. 


the  above  figure,  the  arm  F  W  is  to  F  P  as  1  to  3,  then  the 
power  P  will  be  to  the  weight  W  as  1  to  3.  That  is,  if  the 
length  of  the  longer  arm  is  3  times  that  of  the  shorter  arm,  in 
order  to  produce  an  equilibrium  the  weight  must  be  3  times  the 
power.  In  order  that  the  weight  may  be  raised,  it  is  evident 
the  power  must  be  a  little  increased,  so  as  to  exceed  one-third 
of  the  weight. 

B\  When  motion  is  produced 

J\         by  means  of  this  lever,  the  ex- 
"""    Vw   tremity  of  each  arm  moves  in 
the  circumference  of  a  circle, 
the  centre  of  which  is  at  the 


Fig.  43. 


point  of  support  or  fulcrum,  as 
is  shown  in  figure  43 ;  and  the 
arc  described  by  each  will  be 
in  proportion  to  its  length. 
Consequently,  to  raise  the  weight  any  distance,  as  an  inch,  in 
the  arc  W  B,  supposing  the  longer  arm  3  times  the  length  of 
the  shorter,  the  power  must  fall  in  the  arc  PA  3  times  as  far, 
or  3  inches.  This  is  always  found  to  be  the  case  in  the  use  of 
machines  (§ 122) ;  the  space  passed  over  by  the  power  will  be 
to  that  passed  over  by  the  weight,  as  the  weight  is  to  the 
power. 

117.  Numerous  examples  of  the  use  of  this  kind  of  lever  will 
readily  occur  to  every  one.  The  common  balance,  in  which 
the  arms  are  equal,  and  the  steelyards,  in  which  they  are  un- 
equal, the  scissors,  pincers,  &c.,  are  instances. 

„  In  the  steelyards,  figure  44,  the 

arm  on  which  the  power  or  counter- 
poise is  placed,  is  variable,  so  that 
the  same  power  is  thus  made  to  ba- 
lance different  weights;  this  is  the 
design  of  the  weigher  in  moving  the 
counterpoise  backward  and  for  ward, 
a  figure,  at  the  notch  in  which  the 
Fig.  44.  counterpoise  in  a  given  case  may 

rest,  showing  the  weight  which  it  balances. 

In  the  scissors,  the  intelligent  student  will  readily  determine 
what  is  to  be  considered  the  power,  what  the  weight,  and  what 
the  fulcrum. 


I 


produced  by  means  of  a  lever,  do  the  extremities  of  the  arms  move  in 
straight  lines  ?  In  the  use  of  machines,  how  does  the  space  passed  over  by 
the  power  compare  with  that  passed  over  by  the  weight  ?  117.  What  exam- 
ples of  the  lever  are  mentioned  ?  What  is  the  common  balance  ?  In  the 
common  steelyards,  why  is  the  power  or  counterpoise  made  so  as  to  move 
from  place  to  place  ?  How  is  the  weight  the  counterpoise  balances  in  a  par- 
ticular case,  shown  ?  Do  scissors  act  on  the  principle  of  the  lever  ?  What 
is  to  be  considered  the  power,  what  the  weight,  and  what  the  fulcrum  ? 


MECHANICS.  59 

The  torsion  balance,  which  has  been  referred  to  (§  36)  as 
furnishing  the  necessary  means  of  determining  the  difference 
in  the  weight  of  a  body  at  the  equator  and  at  the  poles,  con- 
sists of  a  coiled  spring  usually  enclosed  in  a  metallic  case.  One 
end  of  it  is  attached  to  a  fixed  support,  and  the  body  to  be 
weighed  is  suspended  from  the  other ;  and  its  weight  is  shown 
by  the  distance  to  which  it  extends  the  spring.  Consequently, 
if  a  body  weighs  more  at  or  near  one  of  the  poles  of  the  earth 
than  at  the  equator,  it  must  extend  the  spring  further  at  the 
former  place  than  at  the  latter.  By  means  of  a  balance  of  this 
kind,  made  with  great  care,  and  transported  from  the  equator 
to  a  high  latitude,  it  is  said  that  the  increased  weight  of  bodies 
in  places  towards  the  poles  has  been  made  plainly  sensible. 

The  description  of  this  balance  is  introduced  here,  so  as  to 
be  in  connection  with  the  remarks  on  the  common  balance, 
and  not  because  it  is  in  any  manner  in  the  mode  of  its  action 
connected  with  the  lever. 

118.  The  second  kind  of  lever  is  distinguished  by  having  the 
power  at  one  extremity,  and  the  fulcrum  at  the  other,  with  the 
weight  between  them. 

In  figure  45,  which  represents  a 
lever  of  the  second  kind,  the  power 

¥~  '  •   II ^p"""  '    is  to  the  weight   as  the  distance 

jrjLy-  from  the  fulcrum  F  to  the  point 

^  where  the  power  is  applied  is  to 

the  distance  from  the  fulcrum  to 

the  point  to  which  the  weight  is  attached ;  that  is,  the  power  is 
to  the  weight  as  F  X  is  to  F  P. 

An  example  of  the  use  of  this  kind  of  lever  is  seen  in  the  case 
of  two  men  carrying  a  burden  on  a  pole  between  them,  one  of 
whom  may  be  considered  the  fulcrum  and  the  other  the  power. 
It  is  evident  the  burden  may  be  so  suspended  between  them 
that  any  given  portion  of  its  weight  may  faH  upon  either  one 
of  them.  As  other  examples  of  this  kind  of  lever,  common  nut- 
crackers, chipping-knives,  and  treadles  to  lathes  may  be  men- 
tioned. 

1 19.  The  third  kind  of  lever  is  that  in  which  the  fulcrum  is 
at  one  extremity,  and  the  weight  or  resistance  at  the  other, 
while  the  power  is  applied  between  them. 


f.  118.  How  is  the  second  kind  of  lever  distinguished  ?  In  figure  45, 
what  is  the  ratio  of  the  power  to  the  weight  ?  What  examples  of  the  use  of 
this  kind  of  lever  are  mentioned  ?  If  two  men  are  carrying  a  weight  on  a 
pole  between  them,  how  must  it  be  placed  so  that  each  shall  sustain  just 
one  half  of  it?  119.  What  is  the  third  kind  of  lever?  In  the  use  of  this 
kind  of  lever,  which  must  be  greatest,  the  power  or  the  weight  ?  Is  the 
object  of  the  lever  always  to  gain  power  ?  When  a  man  raises  a  ladder 
against  the  side  of  a  building,  what  is  to  be  considered  the  power,  weight 
and  fulcrum  ?  Is  he  obliged,  in  raising  it,  to  lift  more  than  its  weight  ?  In 
the  use  of  this  kind  of  lever,  does  the  weight  or  power  move  through  the 


60  NATURAL     PHILOSOPHY. 

It  is  illustrated  in  figure  46,  in 
which  F  is  the  fulcrum  or  prop,  P 
the  power,  and  W  the  weight  as 
before.  In  the  use  of  this  kind  of 
lever,  it  will  be  seen,  there  must  be 
always  a  loss  of  power;  or,  in  other 
words,  the  power  must  always  be  greater  than  the  weight. 

The  object  of  the  lever  is  not,  therefore,  in  all  cases,  to  gain 
power ;  there  may  be  other  motives  for  using  it.  A  man  raising 
a  ladder  against  the  side  of  a  building  is  an  instance  of  the 
third  kind  of  lever ;  the  ladder  itself  is  the  weight,  and  the 
building  against  which  its  foot  is  placed  is  the  prop  or  fulcrum, 
and  the  man  is  the  power.  Now,  he  might  adopt  other  means 
to  raise  the  ladder,  in  which  less  physical  strength  would  be 
required  ;  but  notwithstanding  this  disadvantage,  he  still  finds 
it  more  convenient,  on  the  whole,  to  raise  it  in  this  way  than 
to  resort  to  another  method. 

In  the  use  of  this  lever,  it  will  be  observed,  the  weight  moves 
through  a  greater  distance  than  the  power,  contrary  to  what 
takes  place  when  the  levers  of  the  first  and  second  kind  are 
employed.  Thus,  the  top  of  the  ladder  which  the  man  is  raising 
passes  over  a  much  greater  distance  than  his  hands,  which  are 
considered  the  power.  If,  then,  in  using  the  levers  of  the  first 
two  kinds,  we  may  be  considered  as  exchanging  time  or  velo- 
city for  power,  in  using  this  kind  we  make  the  reverse  ex- 
change, and  gain  time  by  applying  greater  power. 

The  most  striking  examples  of  the  third  kind  of  lever,  we  are 
informed  by  anatomists,  are  found  in  the  animal  economy. 
Most  of  the  limbs  of  animals  are  levers  of  this  description;  the 
socket  of  the  bone  is  the  fulcrum,  a  strong  muscle  attached  to 
the  bone  near  the  socket  is  the  power,  and  the  limb  itself,  with 
any  body  connected  with  it,  is  the  weight.  The  fore-arm,  ex- 
tending from  the  elbow  to  the  wrist,  affords  an  excellent  in- 
stance. The  arm-bone,  which  connects  with  one  of  the  fore- 
arm bones  at  the  elbow,  is  the  fulcrum ;  the  large  muscle  lying 
on  the  fore-side  of  the  arm-bone,  is  the  power;  and  the  hand, 
with  anything  contained  in  it,  is  the  weight.  The  hand  is  raised 
by  the  contraction  of  the  muscle,  the  motion  of  which  can 
readily  be  felt  by  placing  the  left  hand  upon  the  right  arm 
above  the  elbow,  and  then  making  an  effort  with  the  right 
hand,  as  if  to  raise  a  heavy  substance. 

It  is  evident  that,  by  this  arrangement,  to  raise  a  weight  in 
the  hand,  the  force  exerted  by  the  muscle  must  be  much  greater 

greater  distance  ?  Where  do  we  find  the  most  striking  examples  of  this 
kind  of  lever?  In  the  fore-arm,  what  is  the  power,  what  the  weight,  and 
what  the  fulcrum  ?  How  does  the  muscle  raise  the  hand  ?  In  order  to 
raise  the  hand,  must  the  muscle  exert  a  greater  force  than  if  it  were  applied 
directly  to  the  hand  ?  Is  it  essential  that  the  lever  should  be  straight  ? 


MECHANICS.  61 

than  if  it  were  applied  directly  to  the  weight ;  but  this  disad- 
vantage is  more  than  compensated  by  other  advantages  equally 
important. 

It  is  not  essential  that  the  lever  should  always  be  straight; 
it  may  be  curved  in  different  directions,  or  even  bent  at  right- 
angles,  and  the  result  will  be  the  same.  The  hammer  with 
which  a  carpenter  draws  a  nail  from  a  piece  of  wood  may  be 
considered  a  lever,  the  arms  of  which  make  a  right-angle  with 
each  other. 

120.  Simple  levers  are  sometimes  so  combined,  that  one,  in- 
stead of  acting  directly  on  the  weight,  acts  on  a  second,  and 
this  on  a  third,  &c. ;  and  the  last  exerts  the  combined  effect  of 
the  whole  on  the  weight.  Such  a  combination  of  levers  is  called 
a  compound  lever. 

Y  In  figure  47,  we  have 

"F— i,  -=F?  P"          a  system  of  levers  of  this 

4  T'  P"        A    1        kind.     To  calculate  the 

p|§  fftw  rati°  °f tne  power  to  the 

p.  *™      weight,   let   us  suppose 

that  the  long  arm  of  each 

simple  lever  is  just  twice  the  length  of  the  short  arm ;  then  P 
will  be  to  P  as  1  to  2,  and  P  to  P"  as  2  to  4,  and  P"  to  W  as  4 
to  8.  Therefore,  1  pound  at  P  will  just  balance  8  pounds  at  W, 
or  the  power  is  to  the  weight  as  1  to  8. 

121.  The  Wheel  and  Axle.— The  wheel 
and  axle,  as  already  intimated  (§  113), 
is  generally  considered  merely  as  a  mo- 
dification of  the  lever.  It  is  represented 
in  figure  48,  and  consists  of  a  cylinder, 
A,  termed  the  axle,  around  which  a  cord 
is  wound,  turning  on  a  centre,  and  con- 
nected with  a  wheel,  R.  The  resem- 
blance of  this  mechanical  power  to  the 
lever  will  be  best  seen  by  a  side  view 
of  the  wheel,  as  in  figure  49,  in  which 

R  is  the  wheel,  and  A  one  end  of  the  axle,  P  the  power,  W  the 
weight,  and  the  point  of  support  the  fulcrum.  It  is  evident  that 
the  radius  of  the  wheel  AC  becomes  the  long  arm  of  the  lever, 
and  the  radius  of  the  axle  A  B  the  short  arm ;  consequently, 
(§ 116),  the  power  must  be  to  the  weight  as  the  radius  of  the 
axle  is  to  the  radius  of  the  wheel. 

Quest.  120.  What  constitutes  the  compound  lever  ?  If  three  levers  are 
combined  in  this  manner,  each  having  its  longer  arm  twice  the  length  of  the 
shorter,  what  will  be  the  ratio  of  the  power  to  the  weight  ?  121.  What  is 
the  wheel  and  axle  usually  considered  ?  Of  what  two  parts  does  it  consist  ? 
What  is  to  be  considered  the  long  arm  of  the  lever,  and  what  the  short  arm  ? 
What,  will  be  the  ratio  of  the  power  to  the  weight  ?  If  the  wheel  is  turned 
once  round,  how  far  will  the  weight  and  power  move  ?  How  much  greater 

6 


62 


NATURAL     PHILOSOPHY. 


Fig.  49. 


If  we  suppose  the  wheel  to  be  turned  once 
round,  it  is  plain  the  power  will  fall  a  dis- 
tance just  equal  to  the  circumference  of  the 
wheel,  while  the  weight  will  be  raised  a  dis- 
c  tance  equal  to  the  circumference  of  the  axle. 
But  the  circumferences  of  circles  are  to  each 
other  as  their  radii ;  hence  the  distance  pass- 
ed over  by  the  power  is  as  much  greater 
than  that  passed  over  by  the  weight  as  the 
radius  of  the  wheel  is  greater  than  the  radius 
of  the  axle ;  or,  more  correctly  stated,  the 
distance  passed  over  by  the  power  is  to  the 
distance  passed  over  by  the  weight  as  the 
radius  of  the  wheel  is  to  the  radius  of  the 
axle ;  that  is,  as  the  long  arm  of  the  lever  is  to  the  short  arm. 
As  a  necessary  consequence  of  this,  if  we  multiply  the  weight 
by  its  velocity,  or  by  the  distance  through  which  it  moves,  the 
product  will  be  the  same  as  if  we  multiply  the  power  by  its 
velocity.  That  is,  the  momentum  (5  95)  of  the  power  will 
always  be  just  equal  to  that  of  the  weight.  Let  us  suppose,  for 
instance,  that  the  circumference  of  the  wheel  is  9  feet,  and  that 
of  the  axle  3  feet,  then  the  power  will  be  to  the  weight  as  1  to 
3 ;  if  we  turn  the  wheel  round  once,  the  power  will  move  9  feet, 
and  the  weight  3  feet.  But  1  x  9=3  x  3=9. 

122.  The  advantage  of  the  wheel  and  axle  over  the  lever 
consists  in  its  allowing  a  longer  continued  motion  without 
cessation.  Manifestly  it  can  make  no  difference  in  the  princi- 
ple upon  which  this  mechanical  power  acts,  whether  the  force 
is  applied  directly  to  the  rim  of  the  wheel  by  means  of  a  rope, 
or  whether  there  are  pins  in  the  rim  to  be  taken  hold  of  by  the 
hands,  as  in  figure  48,  or  whether  the  axle  is  turned  with  a 
crank  or  a  single  movable  handspike,  as  we  often  see,  in  the 
use  of  the  windlass,  on  board  of  ships. 

/'"R\ 

/  \  Indeed,  in  every  case,  it  is  easy  to 
j  see  that  the  power  describes  a  circle  as 
really  as  when  the  wheel  is  used.  Thus, 
in  figure  50,  the  hand  applied  to  the 
crank  revolves  in  the  circle  R,  and 
the  power  is  to  the  weight  as  the  ra- 
dius of  the  axle  is  to  the  length  of  the 

Pig.  50. 


is  the  distance  passed  over  by  the  power  than  that  passed  over  by  the  weight  f 
If  we  multiply  the  power  by  its  velocity  and  the  weight  by  its  velocity,  how 
will  the  products  compare  ?  122.  In  what  does  the  advantage  of  the  wheel 
and  axle  over  the  lever  consist  ?  Will  it  make  any  difference  in  the  principle 
upon  which  this  machine  acts,  whether  the  power  is  applied  to  the  rim  of  a 
wheel,  or  whether  the  axle  is  turned  by  a  handspike  or  crank  ?  What  is 


MECHANICS, 


63 


The  capstan,  figure  51,  is  merely  an 
upright  axle  with  a  horizontal  wheel,  R, 
or  a  crank,  which  is  equivalent  to  it. 
The  advantage  of  the  capstan  over  the 
ordinary  wheel  and  axle  consists  in  its 
allowing  the  workman  to  walk  around 
it,  as  he  terms  it,  to  move  the  weight. 


Fig.  51. 

123.  Wheels  and  axles  may  be  combined  to  produce  a  com- 
pound machine,  much  in  the  same  manner  as  the  system  of 
levers.  Examples  of  the  kind  are  seen  in  clocks  and  watches, 
and  in  almost  all  kinds  of  machinery. 

Figure  51  a  represents  a  sys- 
tem composed  of  three  wheels 
which  act  upon  each  other  by 
means  of  teeth ;  the  teeth  in  the 
circumference  of  one  wheel  con- 
necting with  those  in  the  axle, 
usually  called  the  pinion,  of  the 
next.  To  estimate  the  mechani- 
cal power  of  such  a  system,  or 
the  ratio  of  the  power  to  the 
weight,  we  have  only  to  multi- 
ply together  the  number  of  teeth 
in  the  wheels,  and  also  the  number  in  the  pinions,  and  the  pro- 
ducts thus  obtained  will  themselves  express  the  ratio  required. 
Suppose  each  of  the  wheels  FEG  to  contain  30  teeth,  or  to  be 
of  sufficient  diameter  to  contain  this  number,  and  each  of  the 
pinions  CB  A  only  5;  then  30x30x30=27000,  and  5x5x5= 
125.  Consequently,  the  power  P  is  to  the  weight  W  as  125  to 
27000;  or,  which  is  the  same  thing,  as  1  to  216.  Therefore,  1 
pound  at  P  will  balance  216  pounds  at  W. 

Instead  of  teeth,  the  wheels  are  often  furnished  with  bands, 
by  the  friction  of  which  the  motion  is  communicated  from  one 
wheel  to  the  other.  In  such  cases  the  wheels  may  be  placed  at 
considerable  distances  from  each  other,  which  is  often  of  great 
importance. 

the  capstan  ?  How  does  it  differ  from  the  wheel  and  axle  ?  123.  How  are 
several  wheels  and  axles  sometimes  combined  so  as  to  act  upon  each  other  ? 
How  are  they  connected  ?  How  is  the  ratio  of  the  power  to  the  weight  to  be 
calculated  ?  If  there  are  three  wheels  with  30  teeth  each,  as  in  figure  51  a, 
with  pinions  having  each  only  5  teeth  connected  together,  how  many  pounds 
at  W  will  be  required  to  balance  1  pound  at  P  ?  How  is  this  number  ob- 
tained ?  Are  the  wheels  always  made  to  act  upon  each  other  by  means  of 
teeth?  Why  are  bands  sometimes  used? 


TV- 


Fig.  51  a. 


64 


NATURAL     PHILOSOPHY. 


Fig.  52. 


124.  The  Pulley. — The  mechanical  power  usually  called  a 
pulley,  in  its  simplest  form,  consists  of  a  wheel  having  a  groove 
in  its  circumference,  so  fixed  in  a  block  as  to  move  freely  upon 
a  pivot  in  its  centre,  and  having  a  cord  or  rope  passing  over  it. 
It  will  be  seen,  however,  as  we  proceed,  that  the  use  of  this 
wheel  is  only  to  diminish  the  friction,  which  without  it  would 
be  so  great  as  to  render  the  machine  quite  useless. 

125.  There  are  two  kinds  of  pulleys, 
the  fixed  and  the  movable.  Figure*52 
is  a  fixed  pulley,  C  the  wheel,  some- 
times called  the  sheave,  R  R  the  cord, 
P  the  power,  and  W  the  weight.  It 
is  very  evident  that  the  power  and 
weight,  to  balance  each  other,  must 
be  exactly  equal;  consequently,  no. 
mechanical  advantage  is  gained  by  it. 
But  it  is  of  great  importance  often  in 
changing  the  direction  of  motion,  as 
it  is  much  easier  for  a  man  to  raise  a 
weight  by  a  rope  passing  over  a  pulley 
than  to  carry  the  weight  up  a  flight 
of  stairs  or  a  ladder,  or  to  go  up  him- 
self, and  then  pull  the  weight  up  after  him. 

126.  A  mere  inspection  of  the  figure 
IB  is  also  sufficient  to  show  that  the  only 
use  of  the  wheel  or  sheave  is  to  diminish 
the  friction;  for  if  the  cord,  S,  figure 
53,  passed  over  a  block  of  wood,  B,  in 
order  that  the  power  and  weight  may 
balance  each  other,  they  must  be  equal. 
But  if  sufficient  power  is  to  be  applied 
to  raise  the  weight,  there  would  be  great 
loss  by  reason  of  the  friction  of  the  cord 
upon  the  wood.  The  cord  and  the  block 
would  also  be  so  rapidly  worn  away  as 
to  render  it  entirely  useless  in  practice. 
Though  no  direct  mechanical  advantage  is  ordinarily  gained 
by  the  use  of  a  fixed  pulley,  yet  a  man  may  raise  himself  by 
means  of  it  by  exerting  a  force  equal  to  only  half  his  weight. 

Quest.  124.  What  is  the  pulley  ?  What  is  the  use  of  the  wheel  ?  125. 
What  two  kinds  of  the  pulley  are  there  ?  How  must  the  power  and  weight 
compare  in  order  to  balance  each  other  over  a  single  fixed  pulley  ?  Why  is 
the  fixed  pulley  still  used  if  no  mechanical  advantage  is  gained  by  it  ?  126. 
What  would  be  the  effect  if  the  cord  was  made  to  pass  over  a  block  of  wood 
instead  of  a  wheel  ?  How  may  a  person  raise  himself  by  means  of  a  fixed 
pulley  ?  What  part  of  his  own  weight  would  he  have  to  draw  up  with  his 


Fig.  53. 


MECHANICS 


65 


Fig.  54. 


Thus,  let  a  man  be  seated  in  a  chair  having 
one  end  of  a  rope  attached  to  it ;  the  other  end, 
after  passing  round  a  fixed  pulley,  returning  to 
his  hand,  as  represented  in  figure  54.  If  he  now 
pulls  downward  by  an  amount  equal  to  half  his 
weight,  he  will  be  supported,  one-half  by  the 
direct  effort  of  his  hands,  and  the  other  half  by 
the  chair.  This  is  sometimes  found  a  very  con- 
venient method  for  a  person  to  let  himself  down 
into  a  well,  and  to  draw  himself  out  again. 


127.  The  movable  pulley  is  represented  in 
figure  55.  In  this,  one  end  of  the  cord  is  at- 
tached to  a  fixed  support,  A,  and  to  the  other 
end  the  power  is  applied.  As  both  parts  of  the 
cord  will  have  an  equal  tension,  it  is  evident 
one-half  of  the  weight  W  will  be  sustained  by 
the  hook  A,  and  the  other  by  the  power  P; 
hence,  the  power  will  be  to  the  weight  as  1  to 
2.  Instead  of  pulling  upward  with  the  hand, 
as  represented  in  the  figure,  it  is  usual  to  have 
the  cord  passed  over  another  fixed  pulley. 


Fig.  55. 


128.  In  raising  a  weight  by  a  single  movable  pulley,  as  just 
described,  it  will  be  seen  the  power  has  to  pass  over  twice  the 
space  which  is  traversed  by  the  weight ;  that  is,  as  in  the  case 
of  the  lever,  (§  116),  or  the  wheel  and  axle,  ($ 121),  the  space 
passed  over  by  the  power  is  to  that  passed  over  by  the  weight 
as  the  weight  is  to  the  power.  That  the  power  has  to  pass 
over  twice  as  much  space  as  the  weight,  will  be  evident  from 
the  consideration  that,  to  raise  the  weight  1  inch,  both  cords 
which  support  it,  or  rather  both  parts  of  the  cord,  must  be 
shortened  an  inch,  which  would  require  the  hand  to  move  2 
inches. 

hands  ?  127.  When  the  fixed  pulley  is  used,  by  how  many  cords  is  the 
weight  supported  ?  How  many  support  it  when  a  single  movable  pulley  is 
used  ?  What  then  is  the  ratio  of  the  power  to  the  weight  ?  128.  When  a 
single  movable  pulley  is  used,  how  much  more  space  must  the  power  pass 
over  than  the  weight  ?  How  does  this  appear  ? 
6* 


NATURAL     PHILOSOPHY. 

129.  Usually,  in  practice,  several  pulleys  are  com- 
bined, as  is  shown  in  figure  56.  Here  are  two  fixed 
pulleys  in  the  block  A,  and  two  movable  ones  in  B ; 
and  the  weight  W  is  sustained  by  four  cords,  or, 
which  is  the  same  thing,  by  four  parts  of  the  same 
cord.   As  all  parts  of  the  cord  are  equally  extended, 
each  of  them  of  course  sustains  one-fourth  part  of 
the  weight ;  or  the  power  P  is  to  the  weight  W  as 
1  to  4.     In  other  words,  a  power  of  1  pound  is  made 
to  counterpoise  a  weight  of  4  pounds. 

In  this  instance  it  will  be  perceived,  that  in  order 
to  raise  the  weight  1  inch,  each  of  the  ropes  must 
be  shortened  an  inch,  which  will  require  the  power 
to  move  through  4  inches ;  which  also  accords  with 
the  maxim  that  what  is  gained  in  power  is  lost  in 
time. 

130.  There  may  be  more  than  two  fixed  and  two 
movable  pulleys  used,  but  in  every  case,  with  a 
single  exception  shortly  to  be  mentioned,  the  power 
will  be  to  the  weight  as  1  to  twice  the  number  of 
movable  pulleys.    Thus,  when  only  one  movable 
pulley  is  used,  the  power  is  to  the  weight  as  1  to  2 ; 
when  there  are  two  movable  pulleys,  they  will  be  to 

Fig.  56.  each  other  as  1  to  4 ;  when  three  are  used,  as  1  to  6, 
and  so  on. 

131.  There  is,  indeed,  one  case,  as  above  intimated,  in  which 
this  rule  requires  to  be  slightly  modified.  In  the  above  figure 
(56)  it  will  be  seen,  the  rope  is  attached  to  the  block  containing 
the  fixed  pulleys  at  C ;  if,  instead  of  this,  it  had  been  attached 
to  the  block  containing  the  movable  pulleys,  as  at  D,  then  it  is 
plain  there  would  have  been  five  ropes  to  sustain  the  weight, 
each  of  which  would  sustain  a  fifth ;  and  the  power  would  be 
to  the  weight  as  1  to  twice  the  number  of  movable  pulleys, 
plus  one ;  or  as  1  to  5.  In  this  case,  one  more  fixed  pulley 
would  have  been  required. 

Instead  of  having  the  pulleys  placed  one  above  another,  as 
represented  in  figure  56,  in  practice  they  are  usually  placed 
side  by  side,  but  the  result  is  the  same. 

Quest.  129.  In  practice,  is  the  pulley  ordinarily  used  singly  ?  When  there 
are  two  fixed  and  two  movable  pulleys,  by  how  many  cords  is  the  weight 
sustained  ?  How  many  pounds  at  W  will  a  power  of  1  pound  at  P  counter- 
poise ?  How  far  must  the  power  P  move  in  order  to  raise  the  weight  1  inch  ? 
How  does  this  appear  ?  130.  When  more  than  two  movable  pulleys  are 
employed,  how  will  the  power  be  to  the  weight  ?  If  there  are  eight  movable 
pulleys,  how  many  pounds  at  W^will  1  pound  at  P  be  sufficient  to  counter- 
poise ?  131.  What  exception  to  this  rule  is  mentioned?  If,  in  figure  56, 
the  cord  was  attached  to  the  movable  block,  what  would  be  the  ratio  of  the 
power  to  the  weight  ?  Is  it  necessary  that  the  sheaves  or  wheels  in  the  same 
block  should  be  placed  one  above  another  ? 


MECHANICS 


67 


Fig.  57  a. 


132.  Sometimes  the  cord,  or  rope,  instead  of  being  entire,  as 
represented  above,  is  divided  into  several  parts,  each  pulley 
hanging  by  a  separate  string,  one  end  of  which  is  attached  to 
a  fixed  beam. 

By  this  arrangement,  which  is  seen  in 
figure  57a,  we  gain  a  great  increase  of 
power,  attended  by  a  corresponding  loss 
of  time.  We  may  estimate  the  power 
gained  as  follows:  First,  the  power  P, 
which  we  will  suppose  1  pound,  exerts 
its  force  on  the  movable  pulley  A,  over 
the  fixed  pulley  P,  the  other  end  of  the 
cord  being  attached  to  the  beam  above. 
The  pulley  A  is  therefore  drawn  upward 
by  a  force  of  2  pounds.  But  the  first 
movable  pulley  A  is  connected  with  the 
second  pulley  B,  by  the  cord  2,  2,  in  the 
same  manner  as  the  weight  P  is  with  A 
by  the  cord  1,1;  consequently,  the  pulley 
B  must  be  drawn  upward  by  a  force  of 
4  pounds.  In  like  manner  it  may  be 
shown  that  the  third  movable  pulley  C 
must  be  drawn  upward  by  a  force  of  8 
pounds.  Or,  we  may  commence  with  the 
weight  W,  which  we  will  suppose  to  be  8  pounds ;  as  it  is  sus- 
tained equally  by  the  two  parts  of  the  cord  4  and  4,  each  part 
must  support  one-half,  or  4  pounds.  So,  the  pulley  B,  which 
sustains  a  weight  of  4  pounds,  is  supported  equally  by  the  two 
cords  2  and  2,  each  of  which  of  course  sustains  one-half,  or  2 
pounds.  In  like  manner  the  pulley  A  is  supported  by  two  cords, 
each  of  which  sustains  1  pound.  By  this  arrangement,  there- 
fore, a  power  of  1  pound  is  made  to  balance  a  weight  of  8 
pounds ;  or,  in  other  words,  the  power  is  to  the  weight  as  1  to 
8.  If  another  pulley  wer^idded,  it  is  evident  the  weight  which 
the  same  power  would  sustain  would  be  doubled,  or  the  power 
would  be  to  the  weight  as  1  to  16. 

In  estimating  the  effect  of  particular  systems  of  pulleys,  we 
have  left  out  of  the  account  the  weight  of  the  blocks  and  pulleys 
themselves,  which  is  sometimes  considerable.  Usually,  they 
operate  against  the  power ;  that  is,  a  portion  of  the  power  is 
required  to  be  expended  to  counterbalance  their  weight ;  but, 
in  some  cases,  they  are  made  to  act  in  favour  of  the  power. 

Quest .  132.  How  is  the  action  of  the  system  of  pulleys  in  figure  57  a  ex- 
plained ?  What  weight  at  W  will  1  pound  at  P  sustain  ?  If  another  pulley 
were  added,  what  would  be  the  ratio  of  the  power  to  the  weight  ?  What  is 
a  system  of  pulleys  called  ?  In  the  above  estimates,  has  the  weight  of  the 
pulleys  themselves  been  taken  into  account  ?  What  is  the  proportion  of  the 
power  to  the  weight  in  the  system  represented  in  figure  57  5  ? 


68  NATURAL     PHILOSOPHY. 

Such  a  case  is  seen  in  figure  57  6.  One  pul- 
ley, it  will  be  seen,  is  fixed ;  but  the  weight 
of  the  other  two  assists  the  power  P  to  coun- 
terbalance the  weight  W.  The  figures  by  the 
side  of  the  cords  show  the  part  sustained  by 
them ;  and  the  power  is  to  the  weight  as  1  to 
7.  In  reality,  however,  a  little  more  must  be 
added  to  the  weight  W  to  counterbalance  the 
two  pulleys. 

Other  modes  of  using  the  pulley  are  not  here 
discussed,  nor  the  various  methods  that  have 
been  adopted  to  obviate  particular  difficulties. 
In  every  system  of  pulleys,  the  same  propor- 
tion, so  often  noticed,  between  the  space  pass- 
ed over  by  the  power  and  that  passed  over 
by  the  weight,  will  be  observed,  (§  122;)  if,  as 
in  the  above  case,  the  weight  is  8  times  the 
power,  then  the  power  will  move  8  times  as 
far  as  the  weight,  and  of  course  its  velocity 
will  be  8  times  that  of  the  weight.    In  practice, 
Fig.  57  b.          a  system  of  pulleys  is  usually  called  a  tackle* 
133.   The  Inclined  Plane.— This  is  nothing  more  than  a  slope 
or  declivity  frequently  used  for  drawing  up  weights.     The  ad- 
vantage gained  by  it  will  always  be  in  proportion  as  the  length 
of  the  plane  is  greater  than  its  height. 

vr  In  the  inclined  plane  B  C, 
figure  58,  let  us  suppose 
that  B  C  is  five  times  A  C  ; 
then,  in  order  to  produce 
an  equilibrium,  the  weight 
W  must  be  five  times  the 
power  P,  the  cord  connect- 
ing them  being  supposed 


Fig.  58. 


to  pass  over  the  fixed  pulley  F.  To  understand  how  this  effect 
is  produced,  the  weight  W  may  be  supposed  to  be  divided  into 
two  parts,  one  of  which,  equal  to  four-fifths  of  it,  is  supported 
directly  by  the  plane  itself,  while  the  other  part,  equal  to  one- 
fifth,  tends  to  carry  it  down  the  plane,  and  is  supported  by  the 
power  P.  If  the  weight  is  drawn  up  from  B  to  C,  it  is  evident 
the  power  P  must  pass  through  five  times  the  perpendicular 
distance  the  weight  W  does.  For,  suppose  the  weight  to  be  at 
B,  and  the  power  at  F,  the  cord  extending  from  P  to  W;  as 
the  weight  W  ascends  from  B  to  C,  rising  perpendicularly  the 

Quest.  133.  What  is  the  inclined  plane  ?  In  what  proportion  will  be  the 
advantage  gained  by  it  ?  If  the  length  of  the  plane  is  five  times  its  height, 
what  will  be  the  ratio  of  the  power  to  the  weight  ?  If  the  power  sustains  but 
one-fifth  of  the  weight,  how  are  the  other  four- fifths  supported  ?  In  drawing 

*  By  sailors,  this  word  is  generally  pronounced  ta-kel. 


MECHANICS, 


69 


Fig.  59. 


distance  A  C,  P  must  descend  a  distance  equal  to  B  C,  which 
is  5  times  AC.  Therefore,  though  it  requires  only  one-fifth  as 
much  force  to  raise  the  body  up  the  inclined  plane  that  would 
be  necessary  to  raise  it  perpendicularly,  yet  it  has  to  move  five 
times  as  far,  and  with  the  same  velocity  it  of  course  would  re- 
quire five  times  as  much  time.  The  same  principle  just  dis- 
cussed, (§  121),  will  again  be  here  noticed. 

The  velocity  a  body  will  acquire  in  falling  down  an  inclined 
plane,  (making  no  allowance  for  friction,)  is  the  same  as  it 
would  acquire  in  falling  freely  through  an  equal  perpendicular 
height.  That  is,  a  body  falling  from  C  to  B,  down  the  inclined 
plane,  will  attain  precisely  the  same  velocity  as  if  it  fell  perpen- 
dicularly from  C  to  A. 

^  B  134.  The  Wedge. — The  wedge  is  composed  of 
two  inclined  planes,  as  A  and  B,  figure  59.  It  is 
little  used  except  in  cases  where  a  great  force  is 
to  be  exerted  only  at  very  small  distances.  The 
advantage  gained  by  it  is  generally  considered  to 
be  in  proportion  to  its  length  as  compared  with 
half  its  thickness.  In  practice,  too,  it  allows  per- 
cussion to  be  used,  instead  of  simple  pressure,  by 
which  the  effect  is  greatly  increased ;  but  its  power 
cannot  be  very  accurately  calculated. 

The  wedge  is  much  used  in  splitting  wood,  (as 
in  figure  60,)  and  other  substances ;  and,  indeed, 
several  of  our  domestic  instruments  are  modifi- 
cations of  it,  as  the  knife,  chisel,  axe,  &c.  Nee- 
dles and  pins  may  also  be  considered  as  very 
acute  wedges. 

135.  The  Screw. — The  screw 
is  always  composed  of  two 
parts,  the  external  and  the  in- 
ternal screw.  The  external 
screw  consists  of  a  cylinder 
with  a  spiral  protuberance 
winding  round  it,  called  the 
thread.  It  is  well  represented 
by  taking  a  cylinder  AB,  figure  61,  and  wind- 
ing round  it  a  piece  of  paper  cut  in  the  form 
of  a  right-angled  triangle.  The  hypothenuse 
of  the  triangle  will  form  the  thread,  which 
differs  in  nothing  from  the  inclined  plane  except  its  spiral  form. 

up  the  weight  through  the  length  of  the  plane,  how  much  farther  perpendi- 
cularly will  the  power  move  than  the  weight  ?  134.  What  is  the  wedge 
composed  of  ?  In  what  cases  is  it  chiefly  used  ?  In  what  proportion  is  the 
advantage  gained  by  it  ?  For  what  purpose  is  the  wedge  much  used  ?  Can 
its  power  be  accurately  calculated  ?  135.  Of  what  two  parts  is  the  screw 
composed  ?  What  does  the  external  screw  consist  of?  How  may  it  be  re- 
presented ? 


Fig.  60. 


Fig.  61. 


70 


NATURAL     PHILOSOPHY. 


Fig.  62. 


of  the  latter  form,  especially  when 
made  of  wood. 


136.  The  internal  screw  is  sometimes 
called  the  nut,  and  consists  of  a  block  with 
a  cylindrical  hole,  having  the  thread  or 
spiral  protuberance  so  cut  inside,  that  the 
thread  of  the  external  screw  will  exactly 
fit  between  them.  In  figure  62,  S  repre- 
sents the  external  screw,  and  N  the  inter- 
nal screw  or  nut. 

The  thread  of 
the  screw  may 
be  cut  square, 
as  in  A,  figure 
63,  or  wedge- 
]  shaped,  as  in  B; 
but  it  is  more 
frequently  seen 


Fig.  63. 


137.  In  using  the  screw  as  a  mechanical  power,  two  motions 
are  necessarily  produced ;  one  of  the  parts  must  be  made  to 
revolve  on  its  axis,  and  one  or  the  other  must  at  the  same  time 
advance  in  the  direction  of  the  length  of  the  cylinder  on  which 
the  external  screw  is  cut.  In  figure  62,  the  external  screw  is 
supposed  to  be  turned  by  means  of  the  handle  L;  and  it  is  plain 
it  must  at  the  same  time  advance  either  upward  or  downward 
according  to  the  direction  in  which  it  is  turned.  But  this  ar- 
rangement is  not  essential ;  the  parts  may  be  so  formed  that 
either  one  may  revolve  and  either  one  advance,  but  not  both 
at  the  same  time.  Whichever  part  is  made  to  revolve,  a  single 
revolution  will  always  cause  an  advance  just  equal  to  the  dis- 
tance between  the  threads.  These  two  motions  of  the  screw 
may  be  well  illustrated  by  grasping  firmly  the  thread  of  a  small 
screw  between  the  thumb  and  finger  of  the  left  hand,  and  turn- 
ing it  at  the  same  time  by  the  right  hand  applied  to  the  head. 
As  it  is  turned,  it  at  the  same  time  passes  through  between  the 
thumb  and  finger  in  the  direction  of  its  length.  Here  both  mo- 
tions are  communicated  to  the  external  screw,  but  this  is  not 
necessary ;  if  the  head  of  the  screw,  as  it  is  termed,  is  held 
against  some  fixed  body,  the  thumb  and  finger,  which  consti- 
tute the  nut,  will  move  in  the  direction  of  the  length  of  the 
screw. 


Quest.  136.  What  does  the  internal  screw  consist  of,  and  what  is  it  called  ? 
In  what  two  forms  is  the  thread  of  the  screw  cut  ?  137.  When  the  screw  is 
used,  what  two  motions  are  produced  ?  In  figure  62,  which  is  supposed  to 
be  turned,  and  which  part  advances  ?  How  far  will  the  screw  advance  by 
a  single  revolution  ?  How  may  these  two  motions  of  the  screw  be  illus- 
trated ? 


MECHANICS 


71 


138.  If  the  screw  were  used  in  this  simple  form  without  a  lever, 
the  advantage  gained  by  it  would  be  in  proportion  as  the  dis- 
tance round  it  is  greater  than  the  distance  between  the  threads, 
the  former  of  which  may  be  considered  the  length  of  the  inclined 
plane,  and  the  latter  its  height  ($  133).  But  the  screw  is  seldom 
if  ever  used  without  a  lever  (as  L,  figure  62)  to  turn  it,  by 
which  its  power  is  greatly  increased.  The  advantage  thus 
gained  by  it  will  be  as  the  circumference  of  the  circle  described 
by  the  end  of  the  lever,  is  to  the  distance  between  the  threads. 

There  are,  therefore,  two  methods  by  which  its  power  may 
be  increased,  either  by  diminishing  the  size  of  the  threads,  or 
by  increasing  the  length  of  the  lever  which  is  used  with  it. 

Let  Us  suppose  it  is  required  to  calculate  the  power  of  a 
screw,  the  threads  of  which  are  ^  of  an  inch  apart,  and  the 
lever  with  which  it  is  turned  is  3^  feet  long,  and  of  course  de- 
scribes a  circle,  when  the  screw  is  turned,  22  feet  in  circumfer- 
ence. The  power  (§ 114)  must  be  to  the  weight  as  the  distance 
between  the  threads  (|  inch)  is  to  the  circumference  of  the 
circle  described  by  the  lever  (22  feet).  We  have  then  the  fol- 
lowing proportion : 

As  £  inch  :  22  ft.^264  inches  : :  1  :  1056;  by  which  it  appears 
that  a  force  equal  to  1  pound  applied  to  the  lever  will  balance 
a  pressure  of  1056  pounds  upon  the  screw.  But  it  is  to  be  ob- 
served that  in  the  use  of  the  screw,  the  loss  from  friction  is  so 
great,  that  its  power  cannot  be  calculated  with  any  considera- 
ble accuracy. 


139.  Sometimes  the  threads  of  a 
screw  are  made  to  act  upon  the 
teeth  of  awheel  so  as  to  turn  it,  as 
in  figure  64;  it  is  then  called  an 
endless  or  perpetual  screw. 

The  screw  is  used  in  almost  an 
endless  variety  of  operations  in 
practical  mechanics,  but  chiefly  in 
cases  where  a  great  pressure  is 
to  be  exerted  through  small  dis- 
tances. 


Fig.  64. 


Quest.  138.  If  the  screw  were  used  without  a  lever,  in  what  proportion 
would  be  the  advantage  gained  ?  When  the  lever  is  used  to  turn  the  screw, 
in  what  proportion  is  the  advantage  gained  ?  By  what  two  methods  may  the 
power  of  the  screw  be  increased  ?  Suppose  the  threads  of  a  screw  are  ith  of 
an  inch  apart,  and  the  lever  with  which  it  is  turned  3^  feet  in  length,  what 
will  be  the  ratio  of  the  power  to  the  weight?  139.  How  is  the  perpetual 
screw  constructed  ?  For  what  purposes  is  the  screw  used  f 


72  NATURAL     PHILOSOPHY. 

140.  Friction. — The  general  subject  of  friction  has  already 
been  referred  to  (§  54),  but  its  important  effect  upon  the  opera- 
tion of  the  mechanical  powers  requires  that  it  should  be  again 
introduced.     Surfaces,  however  well  they  may  be  polished  by 
art,  are  not  perfectly  smooth ;  and  when  they  come  in  contact, 
more  or  less  force  is  always  required  to  cause  one  to  move 
over  the  other,  as  is  necessary  in  the  working  of  machinery. 

141.  In  the  preceding  investigations,  no  allowance  has  been 
made  for  friction,  as  the  object  has  been  merely  to  calculate 
the  ratio  of  the  power  to  the  weight  when  in  a  state  of  perfect 
equipoise;  but,  if  the  weight  is  to  be  raised,  friction  must  ne- 
cessarily be  produced  between  the  different  parts  of  the  ma- 
chinery; and,  in  order  to  overcome  it,  the  power  must  be 
considerably  increased  above  what  has  been  estimated.     As  a 
general  rule,  the  loss  from  friction  is  supposed  to  be  equal  to 
about  one-third  of  the  power  which  is  applied ;  that  is,  if,  by 
the  use  of  a  machine,  a  weight  of  150  pounds  is  exactly  balanced 
by  a  power  of  30  pounds;  then  to  put  the  weight  in  motion 
will  require  an  addition  of  one-third  of  the  original  power,  or 
10  pounds,  making  40  pounds  in  all. 

But  the  resistance  of  friction  in  some  of  the  mechanical 
powers  is  much  greater  than  in  others;  the  lever  is  least 
affected  by  it,  while  in  the  screw  and  wedge  it  is  enormous. 

142.  Friction  is  of  two  kinds,  the  one  occasioned  by  a  body 
gliding  over  another;  the  other  by  the  rolling  of  a  circular 
body.   The  latter  is  usually  much  less  than  the  former.   Owing 
to  this,  friction-rollers  are  sometimes  used  with  the  view  to 
diminish  the  resistance.  So  cylinders  of  wood  are  placed  under 
very  heavy  masses,  as  buildings,  in  moving  them,  for  the  same 
purpose.     Where  rollers  cannot  be  used,  the  rubbing  surfaces 
are  generally  lubricated  by  smearing  them  with  oil  or  grease. 

Quest.  140.  Can  the  surfaces  of  bodies  be  made  perfectly  smooth  by  art  ? 
Why  is  there  always  a  loss  of  power  in  the  use  of  machinery  ?  141.  What 
allowance  for  this  loss  is  usually  to  be  made  ?  If  a  weight  of  150  pounds  is 
balanced  by  the  use  of  a  machine  by  a  power  of  30  pounds,  how  much  addi- 
tional power  will  be  required  to  put  the  machine  in  motion  and  raise  the 
weight  ?  Are  all  the  mechanical  powers  equally  affected  by  friction  ?  Which 
is  least  affected  by  it  ?  142.  What  two  kinds  of  friction  are  there  ?  Which 
is  the  greatest  ?  What  are  friction  rollers  ?  For  what  purpose  are  cylinders 
of  wood  usually  placed  under  buildings  and  other  "heavy  bodies  in  moving 
them  ?  What  is  the  object  of  greasing  the  joints  of  machinery  ? 


HYDROSTATICS.  73 

CHAPTER  II. 
HYDROSTATICS. 

143.  THIS  branch  of  science  treats  of  the  nature,  pressure, 
and  motion  of  fluids  in  general,  and  their  relation  to  solids. 

A  fluid  is  a  substance  that  yields  to  the  slightest  pressure. 
There  are  two  kinds  of  fluids,  liquids  and  gases ;  but  in  this 
chapter  we  propose  to  confine  ourselves  entirely  to  the  former, 

144.  Fluids  are  subject  to  all  the  laws  developed  in  the  pre- 
ceding pages,  only  with  such  modifications  as  depend  upon 
their  peculiar  constitution;  they  obey  strictly  the  laws  of  gra- 
vitation and  motion  in  cases  where  the  ready  mobility  of  their 
particles  does  not  interfere.    A  mass  of  water  or  other  fluid,  in 
falling  from  a  height,  would  produce  the  same  effect  as  an 
equal  mass  of  a  solid,  if  no  opposing  cause  existed ;  and  the 
reason  why  no  one  fears  the  fracturing  of  his  skull  by  the  dash- 
ing of  a  quantity  of  water  upon  him  from  an  elevation,  is  be- 
cause the  particles  are  so  easily  separated  from  each  other ;  the 
mass  is  broken  merely  by  the  resistance  of  the  air,  and  conse- 
quently the  momentum  of  the  whole  cannot  be  made  to  act  on 
a  single  point,  as  is  the  case  with  solids.     If  the  particles  of  the 
mass  are  made  to  cohere  by  freezing,  then  its  mechanical  effects 
will  be  the  same  as  those  of  any  other  solid. 

145.  Liquids  are  slightly  compressible.     This  was  for  a  long 
time  doubted;  but,  from  the  result  of  many  very  accurate  ex- 
periments, it  is  found  that  water,  which  may  be  considered  as 
the  representative  of  liquids  in  general,  is  diminished  in  volume 
about  46  millionths  by  a  pressure  of  fifteen  pounds  to  each 
square  inch.   An  apparatus  has  been  constructed  which  shows 
this  in  a  very  satisfactory  manner. 

Quest.  143.  Of  what  does  the  branch  of  science  called  Hydrostatics  treat? 
What  is  a  fluid  ?  144.  Are  fluids  subject  to  the  laws  which  have  already 
been  discussed  ?  Do  they  obey  the  same  laws  of  gravitation  as  solids  ? 
Why  do  not  fluids  in  falling  produce  the  same  mechanical  effects  as  solids  ? 
If  the  particles  of  water  are  made  to  cohere  by  freezing,  what  would  be  the 
effects  of  the  falling  of  a  mass  ?  145.  Are  liquids  compressible  ?  By  what 
part  of  its  volume  is  water  compressed  by  a  pressure  of  15  pounds  to  the 
square  inch  ?  How  is  the  apparatus  constructed  which  is  used  to  demon- 
strate the  compressibility  of  liquids  ?  When  the  pressure  is  removed,  will 
the  liquid  possess  the  same  volume  as  at  first  ?  Are  all  liquids  equally  com- 
pressible ? 

7 


74 


NATURAL     PHILOSOPHY. 


Fig.  65. 


Let  A  B CD,  figure  65,  be  a  strong  glass  vessel,  having 
firmly  cemented  on  its  upper  part,  A  B,  a  short  metallic 
cylinder,  E  F,  with  a  piston,  G,  fitting  into  it  perfectly 
tight,  and  capable  of  being  moved  up  and  down  by  the 
screw,  H.  K  is  a  bottle,  having  its  neck  drawn  out  into 
a  small  tube,  to  which  a  scale,  L,  is  attached,  graduated 
to  small  parts  of  an  inch.  This  bottle  is  first  to  be  filled 
with  water  quite  to  the  top  of  the  tube,  and  then  a  minute 
globule  of  mercury  is  to  be  introduced,  so  as  to  rest  upon 
the  surface  of  the  water.  Let  us  suppose  that  by  trial  it 
is  found  that  1  inch  of  the  tube  forming  the  neck  of  the 
bottle  is  capable  of  containing  just  80  millionths  as  much 
as  the  bottle.  The  bottle,  with  its  tube  and  scale,  is  now 
to  be  placed  in  the  large  glass  vessel,  which  is  then  to  be 
filled  with  water,  and  the  piston  inserted.  By  turning 
the  screw,  the  piston  is  forced  down,  and  all  the  water, 
both  within  and  without  the  bottle  K,  equally  compress- 
ed ;  and  the  diminution  of  volume  of  that  within  the 
bottle  will  be  indicated  by  the  descent  of  the  globule  of 
mercury  in  the  neck  of  the  bottle  K.  If  the  globule  is 
seen  to  fall  an  inch,  then  it  is  plain  the  water  has  been  compressed  80 
millionths  of  its  volume ;  if  the  globule  is  made  to  fall  2  inches,  the  com- 
pression will  be  160  millionths  of  the  original  volume,  and  so  on.  When 
the  piston  is  raised,  and  the  pressure  removed,  the  globule  of  mercury  will 
rise  to  its  original  position,  showing  that  water  is  really  elastic. 

By  this  means  it  has  been  determined  that  all  liquids  are  compressible ; 
but  each  has  a  compressibility  peculiar  to  itself,  some  being  more  and 
some  less  compressible  than  water. 

146.  In  order  to  determine  the  amount  of  pressure  to  which  the 
liquid  is  at  any  time  subjected,  a  small  glass  tube,  figure  66,  closed 
at  the  top,  and  open  at  the  bottom,  is  placed  inside  the  apparatus 
with  the  bottle  K.     This  tube  being  filled  with  air,  the  water  can- 
not rise  in  it  except  as  it  compresses  the  air  before  it  (§  8),  which  it 
is  known  (as  will  hereafter  appear)  is  diminished  in  volume  by  just 
one-half  for  every  15  pounds*  pressure,  or  one  atmosphere.    Th« 
tube  being  carefully  graduated  to  fractions  of  an  inch,  when  by 
screwing  down  the  piston  the  water  is  seen  to  rise  half-way  in  it, 
we  know  the  pressure  to  be  equal  to  15  pounds  to  the  inch,  which 
is  called  one  atmosphere ;  when  the  water  rises  so  as  to  fill  one- 
g       half  of  the  remainder  of  the  tube,  or  three-fourths  of  the  whole, 
the  pressure  will  be  equal  to  three  atmospheres,  or  45  pounds  to  the  inch, 
and  so  on. 

If  this  seems  obscure  to  the  young  student,  let  him  recollect  that  when 
the  tube  is  placed  in  the  apparatus,  it  is  under  the  pressure  of  1  atmo- 
sphere— the  ordinary  atmospheric  pressure — and  when  this  is  doubled,  or 
the  pressure  increased  to  2  atmospheres,  the  water  will  rise  so  as  to  fill 
half  the  tube.  If  this  pressure  is  again  doubled,  or  the  pressure  increased 
to  4  atmospheres,  one-half  of  the  remaining  space,  or  three-fourths  of  the 
whole  tube,  will  be  filled  with  water ;  but,  in  these  4  atmospheres,  the  ordinary 

Quest.  146.  How  is  the  amount  of  pressure  determined  ?  How  much  is 
the  volume  of  air  diminished  by  a  pressure  of  15  pounds  to  the  inch  ? 


HYDROSTATICS.  75 

atmospheric  pressure  is  included,  so  that  the  pressure  applied  by  the  ap- 
paratus will  be  equal  to  3  atmospheres. 

This  subject  will  be  made  plain  in  the  Chapter  on  Pneumatics. 

147.  Though  the  particles  of  liquids  move  freely  amongthem- 
selves,  there  is,  as  we  have  heretofore  seen,  a  slight  attraction 
between  them,  as  is  shown  by  their  adhering  together  to  form 
the  drop.    But  it  is  very  slight;  and  each  particle  may  there-, 
fore  be  considered  as  gravitating  towards  the  earth  by  itself 
alone,  entirely  independent  of  the  others  by  which  it  is  sur- 
rounded. 

148.  As  a  natural  consequence  of  this,  a  mass  of  any  liquid 
always  takes  the  form  of  the  vessel  in  which  it  is  contained, 
however  irregular  it  may  be.     By  taking  advantage  of  this 
peculiarity  of  liquids,  solids  that  are  capable  of  being  melted 
are  cast  into  any  form  which  is  desired.    The  solid  is  first 
melted,  and  while  in  the  liquid  state  poured  into  a  vessel  or 
cavity  of  the  proper  form  previously  prepared;  and  when  it 
has  solidified  by  cooling,  it  is  found  upon  removal  from  its  bed 
to  be  of  the  shape  required. 

149.  As  another  consequence  of  this  property  of  liquids,  their 
surfaces  will  always  be  found  when  at  rest  to  be  perfectly  level; 
every  particle  at  the  surface  will  be  equally  distant  from  the 
point  to  which  they  all  tend.  This  point,  we  know  (§26),  is  the 
centre  of  the  earth ;  and  hence  the  surface  of  a  fluid  must 
always  partake  of  the  spherical  form  of  the  globe.     This  is 
evident  in  large  bodies  of  water,  as  the  ocean ;  but  the  spheri- 
city of  small  bodies  is  so  trifling  in  consequence  of  the  great 
distance  of  the  centre,  that  their  surfaces  appear  to  the  eye 
perfectly  flat. 

If,  however,  the  extent  of  surface  is  considerable,  its  spherical 
form  becomes  evident.  Thus,  when  a  ship  is  first  seen  in  the 
distance  at  sea,  only  the  tops  of  her  masts  appear  in  view;  but, 
as  she  approaches,  more  and  more  of  her  sails  are  seen,  until 
at  length  the  whole  ship  becomes  visible.  So,  when  the  sailor 
wishes  to  see  a  great  distance,  he  ascends  to  the  mast-head 
with  his  telescope,  knowing  that  in  consequence  of  the  spheri- 
cal form  of  the  surface,  objects  may  be  seen  from  that  elevation 
which  are  entirely  hid  from  his  view  when  upon  the  deck. 

Quest.  147.  Do  the  particles  of  liquids  possess  any  attraction  for  each 
other  ?  How  is  the  slight  cohesion  of  the  particles  shown  ?  How  do  the 
particles  of  liquids  gravitate  ?  148.  Why  does  a  portion  of  a  liquid  in  a  vessel 
always  take  the  form  of  the  inside  of  the  vessel  ?  How  are  metals  and  other 
solids  cast  in  particular  forms  which  may  be  desired  ?  149.  Why  is  the  sur- 
face of  a  liquid  at  rest  always  level  ?  Towards  what  point  does  every  particle 
of  a  liquid  tend  to  fall  ?  Is  the  surface  of  a  liquid  at  rest  a  plane  ?  Why  is 
not  the  convexity  of  the  surface  apparent  in  small  bodies  of  water  ?  Why  is 
the  top  of  the  mast  of  a  ship  at  sea  visible  before  the  lower  parts  ?  Why  does 
a  seaman  ascend  the  mast  of  his  ship  with  his  telescope  when  he  wishes  to 
see  a  great  distance  ?  Suppose  a  line  two  railes  long  drawn  perfectly  straight 


76  NATURAL     PHILOSOPHY. 

But  even  in  bodies  of  water  of  comparatively  limited  extent, 
the  curvature  of  the  surface  is  not  entirely  imperceptible.  If 
we  suppose  a  lake  two  miles  in  diameter  to  be  frozen  over 
with  fine  smooth  ice,  and  a  line  drawn  across  it  perfectly 
straight,  touching  the  ice  in  the  centre,  each  end  of  it  would 
be  no  less  than  8  inches  above  it. 

150.  Pressure  applied  to  Liquids.  —  Liquids,  on  account  of 
the  great  mobility  of  their  particles,  are  capable  of  communi- 
cating any  pressure  exerted  on  them,  equally  in  all  direc- 
tions. 

To  understand  this,  let  ABC  D,  figure  67, 
|C  be  a  vessel  filled  with  water  or  some  other 
liquid,  and  P,  a  solid  piston,  fitting  exactly 
the  inside  of  the  vessel,  so  that  none  of  the 
x  liquid  can  pass  by  it.  For  the  present,  leaving 
Y  the  weight  of  the  liquid  itself  out  of  the  ac- 
z  count,  if  P  weighs  ten  pounds,  this  force  will 
be  sustained  by  the  first  stratum,  x,  of  the 
D  fluid ;  and  this  by  the  next  stratum,  y ;  this 
=»  by  the  next,  z ;  and  so  on  to  the  bottom  of 
the  vessel,  by  which  the  whole  will  be  sup- 
ported. If  the  liquid  were  removed,  the  piston  would  at  once 
descend  and  rest  upon  the  bottom  directly,  by  which  it  would 
be  sustained;  but  this  is  done  as  really  when  the  liquid  is  con- 
tained within,  its  weight  or  pressure  being  transmitted  by  the 
liquid  to  the  bottom. 

If,  while  the  piston  is  in  the  position  represented  in  the  figure, 
the  water  should  be  frozen,  supposing  it  not  to  adhere  to  the 
sides  of  the  vessel,  it  is  plain  that  the  piston  would  rest  upon 
the  ice,  and  the  ice  upon  the  bottom  of  the  vessel ;  or,  in  other 
words,  that  the  pressure  of  the  piston  would  be  transmitted  by 
the  ice  to  the  bottom  of  the  vessel.  But  the  mere  circumstance 
of  the  water  being  frozen  cannot  change  the  transmission  of 
the  pressure ;  the  weight  or  pressure  of  P  must  be  sustained 
by  the  bottom  alike  in  both  cases. 

151.  But  as  the  shape  of  the  fluid  will  conform  to  the  bottom 
of  the  vessel  accurately,  if  the  whole  surface  of  the  bottom  is 
pressed  by  a  force  of  10  pounds,  one-half  of  it  will  of  course 
sustain  5  pounds,  one-tenth  1  pound,  and  so  on ;  that  is,  if  we 
suppose  the  surface  of  the  bottom  of  the  vessel  to  contain  10 
square  inches,  each  inch  will  sustain  a  pressure  of  1  pound. 


over  the  surface  of  a  frozen  lake,  so  as  just  to  touch  the  ice  in  the  middle, 
how  high  would  each  end  be  above  the  ice  ?  150.  In  what  directions  do  fluids 
transmit  a  force  impressed  upon  them  ?  How  is  figure  67  explained  ?  Would 
the  water  as  really  support  the  piston  when  liquid  as  when  frozen?  151.  If 
the  whole  surface  of  the  bottom  is  pressed  by  a  force  of  10  pounds,  how 
much  will  be  the  pressure  upon  one-half  or  one-tenth  of  it  ? 


HYDROSTATICS,  77 

152.  Thus  far  we  have  spoken  only  of  the  pressure  upon  the 
bottom  of  the  vessel ;  but,  in  consequence  of  the  freedom  of  the 
particles  to  move  among  each  other,  the  same  pressure  will  be 
transmitted  to  the  sides  of  the  vessel  also;  and  if  an  aperture  be 
made,  the  liquid  will  gush  out  with  the  same  force  as  if  made 
at  the  bottom.  If  an  aperture  be  made  at  the  side,  just  equal  in 
size  to  the  piston,  the  force  required  to  be  applied  to  a  second 
piston  inserted  in  this  aperture  to  keep  the  liquid  in,  will  be 
precisely  equal  to  the  weight  of  the  first  piston,  or  ten  pounds. 
If  the  aperture  in  the  side  be  only  half  or  a  quarter  as  large  as 
the  piston  P,  and  a  second  piston  inserted,  then  only  a  propor- 
tional force  will  be  required  to  keep  it  in  its  place. 

Again,  if  a  perforation  be  made  in  the  piston  P  itself,  the 
liquid  will  rush  upward  from  below  in  a  jet  d'eau,  which  shows 
that  there  is  also  an  upward  pressure.  Upon  trial,  this  upward 
pressure  would  be  found  precisely  equal  to  the  downward  or 
the  lateral  pressure,  which  proves  that  liquids  transmit  forces 
acting  on  them  equally  in  all  directions. 

153.  Some  very  important  consequences  result  from  this  pro- 
perty of  liquids  to  transmit  force  equally  in  all  directions. 

Let  A  B  C  D,  figure  68,  be  a  close 
vessel,  the  top  of  which  is  horizon- 
tal, and  O  O'  two  apertures  having 
tubes  inserted  in  them,  which  shall 
be  just  an  inch  square  inside ;  and 
let  P  P'  be  pistons  accurately  fitted 
into  these  tubes.  Let  us  now  sup- 
pose the  vessel  filled  with  water, 
and  a  weight  of  1  pound  applied  to 
Fig.  68.  one  of  the  pistons ;  it  is  plain  that 

every  square  inch  of  the  internal 

surface  of  the  vessel  would  receive  a  pressure  of  one  pound, 
which  would  be  shown  by  the  rise  of  the  other  piston,  if  it  were 
not  loaded  by  a  weight  equal  to  that  placed  upon  the  first.  If, 
therefore,  the  whole  internal  surface  of  the  vessel  is  supposed 
to  contain  1000  square  inches,  a  load  of  one  pound  applied  to 
one  of  the  pistons  produces  a  pressure  upon  the  vessel  of  999 
pounds ;  and  so  in  proportion  to  any  other  weight  applied  to 
the  piston. 

Quest.  152.  Is  there  a  pressure  against  the  sides  of  the  vessel  as  well  as 
against  the  bottom  ?  If  an  aperture  was  made  in  the  side  of  the  vessel  of 
equal  size  with  the  piston,  and  a  second  piston  inserted  into  it,  what  weight 
would  be  required  to  keep  it  in  its  place  ?  If  an  aperture  was  made  in  the 
piston  P  itself,  what  would  be  the  result  ?  Would  the  upward  pressure  be 
equal  to  the  downward  or  the  lateral  pressure  ?  153.  If  the  internal  surface 
of  a  vessel  be  supposed  equal  to  1000  square  inches,  and  an  aperture  an  inch 
square  be  made,  and  a  pressure  of  a  pound  be  applied  by  means  of  a  piston, 
how  much  force  will  be  exerted  upon  the  whole  inside  of  the  vessel  ?  If  a 
second  piston  be  inserted  of  the  same  size  of  the  first,  when  the  first  is  loaded 
with  the  weight  of  a  pound,  what  will  be  the  effect  upon  the  second  ? 


78 


NATURAL     PHILOSOPHY, 


Fig.  69. 


154.  In  the  above  case  we  have 
supposed  the  two  pistons  equal; 
but  let  us  suppose  now  that  the 
tube  O',  figure  69,  is  ten  times  as 
large  as  the  tube  O,  and  the  piston 
P'  of  course  ten  times  as  large  as 
P.  If  the  piston  P  be  loaded  with  a 
weight  of  1  pound,  a  correspond- 
ing pressure  will  be  transmitted  to 
every  portion  of  the  internal  sur- 
face of  the  vessel  A  B  C  D ;  but  the 
piston  P'  being  ten  times  as  large 
as  P,  it  will  require  a  load  of  10  pounds  to  counterbalance  the 
1  pound  upon  P.  If  P  be  loaded  with  a  weight  of  100  pounds, 
then  1000  pounds  would  be  required  upon  P'  to  counterba- 
lance it. 

We  have  made  no  allowance  in  these  calculations  for  the 
friction  of  the  pistons,  which,  in  making  the  actual  experiment, 
would  be  very  considerable,  but  would  not  affect  the  principle 
designed  to  be  illustrated. 

155.  It  will  readily  be  perceived  that  in  the  application  of  the 
principle  above  discussed  we  have  the  means  of  producing 
great  pressure  by  the  use  of  a  comparatively  small  force. 

This  is  accomplished  in  the  ma- 
chine called  the  Hydrostatic  or  Hy- 
draulic Press,  figure  70.  A  is  a  small 
cylinder  with  a  solid  piston,  which 
is  worked  by  the  handle  H,  and  from 
the  lower  part  of  it  a  strong  tube,  BT 
extends  to  a  larger  cylinder,  in  which 
a  strong,  heavy  piston,  P,  is  fitted  so 
-  i  ra  ii  ^L_LX^^  accurately  as  to  move  up  and  down 

cT       I  '••  TjilUr  in  Jt  witnout  ajj°wing  any  water  to 

escape  by  it.  C  is  a  tube  leading  to  a 
cistern  of  water.  Now,  if  we  suppose 
the  diameter  of  the  cylinder  A  to  be 
1  inch,  and  that  of  the  other  cylinder 
6  inches,  the  surface  of  the  lower  end 
of  the  piston  P  will  be  36  times  that 
of  the  small  piston  in  the  cylinder  A; 
and  a  weight  of  1  pound  applied  on 


Fig.  70. 


the  small  piston  will  produce  a  pressure  upon  P,  tending  to 
raise  it,  of  36  pounds.  But  as  the  handle  H  acts  as  a  lever,  a 
man  can  easily,  by  means  of  it,  apply  a  force  of  several  hun- 

154.  If  we  suppose  the  piston  O'  to  be  10  times  as  large  as  O,  how  many 
pounds  upon  P'  will  be  required  to  counterbalance  1  pound  applied  to  P  ? 
Is  any  allowance  made  for  the  friction  of  the  piston ?  155.  How  is  the  Hy- 
draulic Press  constructed  ?  If  the  smaller  cylinder  is  1  inch  in  diameter, 
and  the  larger  6  inches,  how  many  pounds  applied  to  the  larger  piston  will  1 
pound  applied  to  the  smaller  counterbalance  ?  If  by  means  of  a  lever  a  man 


HYDROSTATICS.  79 

dred  pounds,  which  will  be  increased,  as  we  have  seen,  36 
times  by  the  action  of  the  machine.  Let  us  suppose  the  man, 
by  resting  his  whole  weight  upon  the  handle  H,  produces  a 
pressure  of  400  pounds  upon  the  piston  in  A,  then  the  piston  P 
will  be  raised  by  a  force  equal  to  400x36=14400  pounds. 

The  power  of  such  a  machine  may  be  increased  by  diminish- 
ing the  size  of  the  small  piston,  by  increasing  the  larger  piston, 
or  by  increasing  the  length  of  the  handle  H.  There  is,  there- 
fore, scarcely  any  limit  to  the  force  it  may  be  made  to  exert. 

156.  It  is  remarkable,  that  in  this  machine  also,  the  space 
passed  over  by  the  power  will  always  be  to  that  passed  over 
by  the  weight,  as  the  weight  is  to  the  power.  (§  129.)     For,  as 
the  large  cylinder  is  36  times  that  of  the  smaller,  when  the 
small  piston  is  forced  down  one  inch,  the  water  driven  by  it 
into  the  larger  cylinder  will  fill  it  up  only  Jg  of  an  inch,  and  con- 
sequently the  larger  piston  P  will  be  raised  only  that  distance. 

157.  Pressure  produced  by  the  Weight  of  Liquids. — It  is  to  be 
observed  that  thus  far  we  have  spoken  only  of  pressure  which 
may  be  applied  to  a  liquid,  leaving  entirely  out  of  account  the 
weight  of  the  liquid  itself,  and  the  pressure  resulting  from  it. 
This  we  will  now  proceed  to  consider. 

It  is  evident  a  portion  of  the  liquid  in  a  vessel  may  be  sup- 
posed to  constitute  the  piston  P,  figure  67,  for  its  pressure  upon 
the  portion  below  it  will  be  just  the  same  as  if  it  were  solid, 
and  the  pressure  will  be  transmitted  in  the  same  manner  to 
the  bottom  and  sides  of  the  vessel. 

158.  Let  ABC  D,  figure  71,  be  a  vessel 
with  upright  sides  filled  with  water  or  other 
!F  liquid.    Let  us  suppose  a  portion  of  the 
liquid  A  E  F  B  separated  from  the  liquid 


below  by  a  thin  film  EF,  of  some  sub- 
stance ;  it  is  plain,  as  has  been  remarked, 
the  pressure  of  the  upper  portion  thus  se- 
parated from  the  rest  upon  the  part  below, 
will  be  the  same  as  if  it  were  solid ;  for  its 
weight  will  be  sustained  by  it.  Now,  let 
Fig.  71.  us  SUppose  another  portion  of  the  liquid 

EGH  F,  equal  to  the  first,  is  in  like  manner  separated  by  a  film 
G  H,  from  the  part  below ;  it  is  evident  this  will  exert  a  pressure 
equal  to  that  of  the  first  portion ;  and  the  whole  pressure  on 
the  surface  G  H  will  be  twice  as  great  as  that  at  the  surface 

can  apply  400  pounds  to  the  smaller  piston,  how  much  force  will  be  exerted 
upon  the  larger  ?  How  may  the  power  of  the  hydraulic  press  be  increased  ? 
156.  What  is  the  proportion  between  the  distance  passed  over  by  the  power 
and  that  passed  over  by  the  weight  ?  How  does  it  appear  that  when  the 
power  moves  1  inch,  the  piston,  and  of  course  the  weight,  will  be  raised  only 
^th  of  an  inch  ?  157.  Thus  far,  have  we  been  speaking  of  pressure  applied 
to  the  surface  of  a  liquid,  or  of  the  pressure  resulting  from  the  weight  of  the 
liquid  itself?  May  we  consider  a  portion  of  the  liquid  itself  as  constituting 
the  piston  in  figure  67  ?  158.  How  is  figure  71  explained  ?  How  does  the 


80 


NATURAL     PHILOSOPHY. 


EF.  If  below  this  we  should  take  a  third  similar  portion  of 
the  fluid,  the  pressure  upon  the  surface  on  which  that  would 
rest  would  be  three  times  that  of  the  first  portion,  and  so  of 
any  other  proportion. 

It  will  be  seen,  therefore,  the  pressure  of  the  fluid  in  the  vessel 
increases  as  we  descend  exactly  in  proportion  to  the  depth  or 
distance  perpendicularly  below  the  surface. 

We  have,  then,  this  principle,  viz :  the  pressure  of  a  liquia 
at  different  distances  below  the  surface  is  always  proportional 
to  these  distances. 

159.  This  pressure,  it  will  be  observed,  at  any  given  point,  is 
nothing  more  than  the  weight  of  the  liquid  above  that  point ; 
and  of  course  the  heavier  the  liquid  is,  the  greater  will  be  the 
pressure,  the  distance  below  the  surface  being  supposed  the  same. 
The  pressure  of  mercury,  therefore,  is  greater  than  that  of  water, 
and  the  pressure  of  water  greater  than  that  of  alcohol  or  ether. 

It  is  to  be  observed  too,  that  though  the  pressure  of  liquids 
increases  in  proportion  to  the  distance  below  the  surface,  still, 
at  any  given  mathematical  point,  it  will  be  equal  in  every  direc- 
tion ;  that  is,  at  this  point,  the  upward,  downward,  and  lateral 
pressure,  will  be  precisely  the  same.  But,  if  we  take  any  ap- 
preciable portion  of  surface,  unless  it  be  horizontal,  this  will 
not  be  the  case,  as  the  downward  pressure  will  be  greatest. 
But  this  will  shortly  be  explained  more  fully. 

160.  The  pressure  on  the  bottom  of  a  vessel  filled  with  a 
liquid  is  equal  to  the  weight  of  a  column  of  the  liquid  whose 
base  is  equal  to  that  of  the  vessel,  and  whose  height  is  the  same 
as  the  depth  of  the  fluid  in  the  vessel.    It  is,  therefore,  inde- 
pendent of  the  shape  of  the  vessel. 

This  may  be  proved 
experimentally  in  several 
ways;  but  the  following 
apparatus  is  as  simple  as 
any  that  is  used  for  the 
purpose:  ABC, figure 72, 
is  a  glass  tube,  having  a 
brass  collar  cemented  on 
at  A,  into  which  vessels 
of  different  shapes,  D,  E, 
and  F,  may  be  screwed. 
The  tube  ABC  is  filled 
with  mercury  up  to  the 
dotted  line  AC,  and  the 


Fig.  72. 


pressure  increase  with  the  depth  ?  How  will  the  pressure  of  a  liquid  vary  at 
different  distances  below  the  surface  ?  159.  From  what  does  this  pressure 
result  ?  Will  the  pressure  of  all  liquids  be  the  same  at  the  same  depth  ? 
Though  the  pressure  increases  as  we  descend  below  the  surface,  will  it 
always  be  the  same  in  every  direction  at  any  given  point  ?  160.  What  is 
the  pressure  upon  the  bottom  of  a  vessel  filled  with  a  liquid  equal  to  ?  Is 
this  pressure  independent  of  the  form  of  the  vessel  ?  How  may  this  be 


HYDROSTATICS. 


81 


small  tube,  G,  fitted  into  C,  having  its  lower  end  extended  just 
to  the  mercury.  The  vessel,  D,  is  then  screwed  on  A,  and 
water  poured  in  until  it  rises  to  h.  The  surface  of  the  mercury 
at  A  will  be  the  base  of  the  column  of  water,  and  will  of  course 
be  forced  downward  by  the  weight  of  the  water,  and  made  to 
rise  in  G,  we  will  suppose,  to  the  point  p.  If  we  now  unscrew 
D,  and  substitute  either  of  the  other  vessels,  E  or  F,  or,  indeed, 
one  of  any  other  shape,  and  fill  it  with  water  to  h,  on  examining 
the  mercury  in  the  tube,  G,  it  will  be  found  to  rise  exactly  to  p, 
proving  conclusively  that  the  pressure  exerted  by  fluids  is  inde- 
pendent of  their  quantity,  and  varies  only  with  the  perpendicu- 
lar height,  the  base  being  the  same  in  each  case.  In  the  case 
of  the  funnel-shaped  vessel,  E,  the  inclined  sides  support  part 
of  the  weight  of  the  fluid ;  and  when  the  small  vessel,  F,  is  used, 
a  part  of  the  down  ward  pressure  is  counterbalanced  by  an  up- 
ward pressure  against  the  sides  of  the  vessel  where  its  diameter 
is  diminished. 

161.  By  availing  ourselves  of  this  law,  a  very  powerful  force 
may  be  exerted  by  a  small  quantity  of  liquid.  If,  for  instance, 
a  cask  be  filled  with  water,  and  a  small  tube,  say  {  of  an  inch 
in  diameter,  and  20  feet  long,  be  closely  inserted  in  the  bung- 
hole,  and  water  poured  in,  the  pressure  will  be  sufficient  to 
burst  the  cask. 

The  well-known  philosophic  toy, 
called  the  hydrostatic  bellows,  illus- 
trates the  same  fact;  this  consists  of 
two  flat  boards,  B  C  and  D  E,  figure  73, 
united  by  leather,  A.  A  short  tube 
communicates  with  the  interior  of  the 
bellows,  and  terminates  in  a  fawcet,  by 
which  the  water  used  in  the  experiment 
is  drawn  off.  From  this  short  tube  a 
long  tube,  T,  rises  perpendicularly,  and 
terminates  in  a  funnel,  F.  The  upper 
board,  B  C,  is  loaded  with  weights,  W, 
which  press  it  against  the  lower  board, 
DE;  the  leather  which  unites  them 
being  collected  in  folds  between  them. 
If  now  water  is  poured  into  the  funnel 
F,  it  will  descend  and  enter  between 
the  boards;  and,  by  continuing  the 
supply,  a  column  will  be  maintained  in 
the  tube,  which,  by  its  pressure,  will 
gradually  raise  the  upper  board  with 
its  load  as  high  as  the  leather  which  unites  the  boards  will  permit. 

proved  by  means  of  the  apparatus  represented  in  figure  72  ?  In  the  case  of 
the  funnel-shaped  vessel  E,  how  is  a  part  of  the  weight  supported  ?  161. 
How  may  a  very  powerful  force  be  exerted  by  a  small  quantity  of  water  ? 
How  is  the  hydrostatic  bellows  constructed  ?  How  are  the  weights  raised 


Fig.  73. 


82 


NATURAL     PHILOSOPHY. 


162.  In  the  hydrostatic  bellows  we  see  the  powerful  upward 
pressure  of  the  column  of  water  within,  which  is  equal  to  the 
weight  of  a  column  of  water  having  the  upper  board,  B  C,  for 
its  base,  and  its  height  equal  to  the  perpendicular  distance  from 
the  surface  of  the  water  in  the  tube  to  the  lower  surface  of  the 
upper  board.    The  pressure  of  the  water  in  the  tube,  it  will 
be  seen,  serves  the  same  purpose  as  the  small  piston  in  the 
hydraulic  press   (§155);   and   by   increasing  sufficiently   the 
length  of  the  tube,  any  amount  of  pressure  can  be  produced. 

On  account  of  this  upward  pressure  of  liquids,  if  a  hole  is  made 
in  the  bottom  of  a  ship,  the  water  rushes  in  with  great  force. 

163.  We  have  heretofore  seen  (§  159)  that  the  pressure  of  a 
liquid  at  any  point  is  the  same  in  every  direction,  and  is  pro- 
portional to  the  depth  beneath  the  surface.  We  have  seen,  too, 
that  in  the  case  of  pressure  applied  to  a  liquid,  the  force  exert- 
ed on  any  part  of  the  inside  surface  will  be  in  proportion  to 
the  extent  of  that  surface  ($  151) ;  that  is,  if  we  are  able  to  de- 
termine the  amount  of  the  pressure  on  one  square  inch  of  the 
surface,  it  will  be  twice  as  much  on  2  square  inches,  three 
times  as  much  on  3  square  inches,  &c.     So,  the  upward  or 
downward  pressure  of  a  liquid  itself  on  any  surface,  at  any 
given  depth,  will  be  proportional  to  the  extent  of  the  surface, 
and  will  be  entirely  independent  of  the  form  of  the  vessel  (§  1 60). 
But  the  same  cannot  be  said  of  any  portion  of  the  surface  of 
the  sides  of  a  vessel  filled  with  liquid.    From  what  has  been 
said  above  (§  160),  it  is  evident  that  the  pressure  upon  the 
bottom  of  a  vessel,  whatever  its  form,  is  always  just  the  same 
as  it  would  be  if  the  sides  were  upright,  and  the  vessel  was  all 
the  way  of  the  same  diameter  as  at  the  bottom. 

Let  A  B  C  D,  figure  74,  be  a  vessel  with 
upright  sides,  just  a  foot  square,  and  two 
feet  high.  If  this  be  now  filled  with  water 
(or  other  liquid),  the  pressure  upon  the 
bottom  would  evidently  be  equal  to  the 
weight  of  the  liquid;  if  we  supposed  it  filled 
half  full  to  the  line  u  v,  then  the  pressure 
would  be  only  half  as  much,  but  still  would 
be  just  equal  to  the  weight  of  the  liquid. 
C  If  we  now  suppose  the  vessel  filled  with 


water,  and  take  a  point,  as  6,  in  the  middle 
of  uv,  the  pressure  just  that  point  will  be 
equal  in  every  direction  ;  but  if  we  take  a 

that  are  placed  on  the  upper  board  ?  162.  What  is  the  upward  pressure  in 
the  hydrostatic  bellows  equal  to?  Why  does  water  rush  into  a  ship  when  a 
hole  is  made  in  the  bottom  ?  163.  Is  the  pressure  of  a  liquid  on  the  inside  of 
a  vessel  proportional  to  the  extent  of  surface  ?  What  will  be  the  pressure  upon 
the  bottom  of  a  vessel  ?  If  it  have  upright  sides,  will  the  pressure  of  the  liquid 
on  its  bottom  always  equal  the  weight  of  the  liquid?  If  in  the  side  of  the  vessel, 
fig.  74,  we  take  a  space  equal  in  extent  to  the  bottom,  will  the  pressure  be  the 
same  as  upon  the  bottom  ?  What  reason  can  be  given  ?  If  a  cubical  vessel  be 


HYDROSTATICS.  83 

portion  of  the  surface,  as  the  space  C  v  u  O,  which  will  be  of 
the  same  size  as  the  bottom  of  the  vessel,  the  pressure  upon  it 
will  not  be  equal  to  the  whole  weight  of  the  liquid,  as  is  the 
case  with  the  pressure  upon  the  bottom.  Nor  will  the  pressure 
be  equal  on  all  parts  of  the  space  CvuO,  for  the  reason  that 
all  parts  of  it  are  not  equally  distant  from  the  surface  of  the 
liquid.  Near  the  bottom  it  is  evident  the  depth  beneath  the 
surface  of  the  water  will  be  nearly  two  feet,  while  along  the 
line,  u  v,  the  depth  will  be  only  one  foot.  Between  the  lines 
uv  and  CO,  the  parts  would  be  at  different  depths,  and  of 
course  subjected  to  different  pressures. 

If  a  cubical  box  be  filled  with  water,  it  is  found  the  pressure 
on  one  side  is  just  equal  to  half  that  upon  the  bottom;  that  is, 
the  pressure  is  the  same  as  it  would  be  if  the  side  were  changed 
into  a  horizontal  bottom,  and  half  the  depth  of  liquid  rested  on 
it.  The  whole  pressure  of  the  liquid  in  the  vessel  will  therefore 
be  equal  to  three  times  its  weight. 

If  the  vessel  is  made  twice  as  high  as  it  is  broad,  like  that 
represented  in  figure  74,  the  pressure  against  one  side  would 
be  just  equal  to  the  weight  of  the  liquid,  and  the  whole  pressure 
would  amount  to  five  times  its  weight.  While,  therefore,  the 
pressure  of  a  liquid  on  the  inside  of  a  vessel  containing  it  can 
never  be  less  than  its  own  weight,  it  may  be  increased  to  any 
number  of  times  that  weight,  simply  by  increasing  the  height 
of  the  vessel. 

In  consequence  of  the  increasing 
pressure  of  water  as  the  depth  in- 
creases, dams  and  embankments  to 
contain  it  are  always  made  much 
Fi    75  thicker  at  the  bottom  than  at  the 

top,  as  shown  in  figure  75. 

164.  The  pressure  of  liquids  at  very  considerable  depths  be- 
low the  surface  is  enormously  great.  If  an  empty  bottle  tightly 
corked  is  sunk  by  means  of  weights  attached  to  it  to  a  consi- 
derable depth  in  the  sea,  the  pressure  of  the  surrounding  water 
will  either  break  it  by  bursting  it  inward,  or  it  will  force  the 
cork  into  it  through  the  neck,  or  the  water  may  be  forced  in 
through  the  cork.  If  the  bottle  has  flat  sides,  it  will  be  likely 
to  be  broken,  this  form  not  being  conducive  to  strength. 

In  one  case,  a  bottle  tightly  corked,  and  the  cork  covered 
with  pitch,  was  let  down  into  the  sea,  and  on  reaching  the 
depth  of  about  300  feet,  an  increase  of  weight  was  suddenly 

filled  with  water,  how  does  the  pressure  upon  one  side  compare  with  that  upon 
the  bottom  ?  What  will  the  whole  pressure  of  the  liquid  be  equal  to  ?  If  the 
vessel  were  made  twice  as  high  as  it  is  wide,  how  would  the  pressure  upon 
one  side  compare  with  that  upon  the  bottom  ?  How  may  the  whole  pressure 
of  a  given  quantity  of  liquid  be  increased  at  pleasure  ?  Why  are  dams  and 
embankments  always  made  much  thicker  at  bottom  than  at  the  top?  164.  What 
is  the  effect  of  sinking  bottles  tightly  corked  to  great  depths  in  the  sea  ?  Why 
is  the  bottle  likely  to  be  broken  if  it  has  flat  sides  ?  May  the  water  sometimes 


84  NATURAL     PHILOSOPHY. 

felt,  which  proved  to  be  occasioned  by  the  cork  having  been 
forced  in,  and  the  bottle  of  course  filled  with  water.  Another 
bottle  was  let  down  in  a  similar  manner,  which,  on  being  drawn 
up,  was  found  filled  with  water,  though  the  cork  remained  in 
its  place,  the  water  no  doubt  having  been  forced  in  through 
the  cork  or  around  its  sides. 

If  a  piece  of  wood  that  easily  floats  at  the  surface  is  let  down 
by  means  of  a  weight  attached  to  it  to  a  great  depth,  the  water 
will  be  forced  into  its  pores,  and  increase  its  weight  so  much, 
that  it  will  no  longer  be  capable  of  floating  or  rising  to  the 
surface. 

A  diver  may  descend,  with  impunity,  to  a  certain  depth  in 
the  sea,  but  there  is  a  limit  beyond  which  the  pressure  cannot 
be  endured ;  and  it  is  probable  that  even  fishes,  though  fitted 
by  nature  to  sustain  greater  pressures  than  land  animals,  can- 
not exist  beyond  certain  comparatively  limited  depths.  They 
have,  however,  in  some  instances,  been  caught  so  far  beneath 
the  surface,  that  they  must  have  sustained  a  pressure  of  many 
tons  to  every  square  foot  of  the  surface  of  their  bodies. 

165.  Liquids  being  slightly  compressible,  as  we  have  seen,  must  become 
more  dense  at  considerable  depths  than  they  are  at  the  surface.  According 
to  Mrs.  Somerville,  (Connection  of  the  Physical  Sciences,  Section  XI.)  the 
density  of  water  is  doubled  at  the  depth  of  93  miles,  and  it  becomes  as 
dense  as  mercury  at  the  depth  of  362  miles.    At  greater  depths  its  density 
of  course  is  still  greater. 

166.  We  have  seen  ($  149)  that  the  surface  of  a  liquid  in  a 
vessel  at  rest  always  attains  a  perfect  level ;  and  the  same  will 
be  true  if  the  liquid  is  contained  in  several  vessels,  provided 
there  is  a  free  communication  by  means  of  a  tube  or  otherwise 
between  them.    If  the  vessels  be  large,  and  the  tube  uniting 
them  small,  it  may  require  some  time ;  but,  in  every  case,  a 
perfect  level  in  all  the  vessels  will  at  length  be  attained. 

.  _  _.         B      E    P  Every  one's  daily  observation 

is  perhaps  sufficient  to  satisfy 
him  of  this  fact ;  but  the  follow- 
ing piece  of  apparatus,  figure  76, 
has  been  contrived  to  illustrate 
it.  A,  B,  C,  D,  E,  F,  are  several 
glass  vessels  of  different  shapes, 

connected  at  the  bottom  by  a  flat 

Fig.  76.  horizontal  tube,  L  U.   Let  water 

be  now  poured  into  one  of  the 

vessels,  and  it  will  be  seen  to  rise  in  all  alike,  and  stand  at  the 

be  forced  in  through  the  cork  or  by  its  sides  ?  If  a  piece  of  wood  is  sunk  to 
a  considerable  depth  in  water,  why  will  it  not  rise  again  to  the  surface  ?  May 
divers  descend  to  any  depth  beneath  the  surface  ?  Have  fishes  the  power 
of  enduring  greater  pressure  than  man  can  ?  165.  Are  liquids  compressible  ? 
What  then  must  be  the  effect  upon  their  density  at  great  depths  ?  166.  Will 
the  surface  of  a  liquid  in  several  vessels  communicating  together  be  at  the 
same  level  in  all  ?  How  is  this  shown  by  figure  76  ? 


HYDROSTATICS.  85 

same  level,  notwithstanding  the  difference  in  their  forms.  A 
teapot,  kettle,  or  other  vessel  having  a  spout,  to  contain  a 
liquid,  must  have  the  lip  of  the  spout  at  least  as  high  as  the 
level  of  the  liquid  within ;  otherwise  the  liquid  will  flow  out. 

167.  It  is  well  known  that  in  digging  wells  in  the  vicinity  of 
each  other,  we  are  not  always  obliged  to  penetrate  to  the  same 
depth  in  order  to  find  a  supply  of  water ;  nor  is  the  surface  of 
the  water  beneath  the  soil  everywhere  at  the  same  level,  as  the 
principles  we  have  just  discussed  would  seem  to  require.     We 
sometimes  see  wells  but  a  few  rods  apart,  both  of  which  per- 
haps contain  water  during  the  year,  though  the  bottom  of  one 
of  them  is  scarcely,  if  at  all,  lower  than  the  mouth  of  the  other. 

Thus,  let  A  and  B,  figure  77,  be  two 
wells  dug  in  the  hill  side  C  D ;  the 
bottom  of  A  is  above  the  level  of  the 
mouth  of  B,  and  yet  A  may  be  half- 
filled  with  water  at  the  same  time  that 
it  stands  much  below  the  mouth  of  B. 
But  this  in  reality  furnishes  no  excep- 
F.  ?7  tion  to  the  general  law  that  the  surface 

of  a  body  of  water  or  of  several  bodies 

communicating  with  each  other,  will  be  at  the  same  level.  The 
reason  why  the  surface  of  the  water  that  percolates  everywhere 
through  the  soil  is  not  at  the  same  level,  like  the  surface  of  the 
ocean,  may  be  because  of  the  obstructions  that  prevent  its  free 
passage  from  place  to  place,  or  because  of  the  capillary  action 
(§  16)  of  the  soil  itself.  If  the  earth  between  the  wells  A  and  B 
is  very  hard,  or  composed  mostly  of  clay,  which  is  impervious 
to  water,  then  the  wells  may  be  considered  as  two  separate 
vessels,  in  which  we  should  not  of  course  expect  the  water  to 
be  necessarily  at  the  same  level.  But  if  the  earth  at  the  parti- 
cular place  is  of  such  a  nature  as  to  allow  the  water  to  pass 
freely,  it  may  by  capillary  action  be  maintained  at  a  higher 
level  at  one  point  than  at  another. 

168.  The  solution  of  the  hydrostatic  paradox,  as  it  has  been 
called,  will  now  be  easy.     As  usually  stated,  it  is  as  follows, 
viz :  "  Any  quantity  of  water,  however  small,  may  be  made  to 
balance  any  other  quantity,  however  large."     To  make  a  very 
small  quantity  of  water  balance  a  very  large  quantity,  it  is  ne- 
cessary only  to  have  two  vessels  communicating  by  a  tube  at, 
the  bottom,  and  of  such  a  form  that  the  small  quantity  in  the 
small  vessel  shall  stand  in  it  at  the  same  height  as  the  larger 

Quest.  167.  Must  wells  in  the  vicinity  of  each  other  be  always  dug  to  the 
same  depth  to  obtain  water  ?  How  is  this  illustrated  in  figure  77  ?  Does 
this  furnish  any  exception  to  the  law  above  given  that  the  surface  of  a  fluid  ia 
always  level  ?  Why  is  not  the  surface  of  the  water  contained  in  the  soil 
level  ?  168.  What  is  meant  by  the  hydrostatic  paradox  ?  How  may  a  small 
quantity  of  a  liquid  be  made  to  balance  a  much  larger  quantity  ?  Suppose  it 
8 


86 


NATURAL     PHILOSOPHY. 


quantity  in  the  large  vessel.  Suppose  it  were  required  to  make 
a  cubic  inch  of  water  sustain  or  balance  a  cubic  foot,  or  1728 
cubic  inches. 

Let  ABD  and  C  E,  figure  78,  be  two 
cylindrical  vessels  standing  side  by  side, 
and  communicating  with  each  other  by  a 
small  tube ;  and  let  the  diameter  of  the  first 
be  such  that  the  upper  surface  of  the  water 
in  it  shall  be  1728  times  the  surface  of  the 
liquid  in  the  other,  and  the  object  will  be 
3:E  accomplished.  For  if  the  two  vessels  are 
cylindrical,  the  bottom  or  section  of  one  be- 
ing 1728  times  that  of  the  other,  it  is  evident  that  whatever  may 
be  the  height  of  the  water  in  one,  it  must  be  at  the  same  height 
in  the  other.  If  it  is  required 'that  a  still  smaller  quantity  than 
a  single  cubic  inch  shall  balance  the  cubic  foot,  it  is  necessary 
only  that  the  diameter  of  the  smaller  vessel  should  be  propor- 
tionally diminished. 

169.  The  methods  adopted  for  conducting  water  in  canals 
through  a  country  depend  on  the  above  property,  by  which 
liquids  find  their  own  level.  When  the  space  through  which  a 
canal  is  to  be  conducted  is  a  uniform  plain,  there  is  of  course 
no  difficulty ;  but  when  the  surface  is  uneven,  locks  are  re- 
quired, which  are  large  reservoirs  capable  of  containing  the 
boats  that  navigate  the  canal,  and  having  large  gates  at  each 
end,  so  that  they  may  be  filled  and  emptied  at  pleasure.  When 
a  boat  is  to  ascend,  the  lower  gate  is  opened,  and  the  lock  or 
reservoir  emptied,  so  that  the  water  in  it  stands  on  a  level  with 
that  in  the  canal  below,  while  the  upper  gate  prevents  the  water 
entering  from  the  canal  above.  As  soon  as  the  boat  enters  the 
lock,  the  lower  gate  is  closed,  and  the  upper  one  opened ;  and, 
the  water  from  above  entering,  soon  fills  it  to  a  level  with  that 
in  the  canal  above,  the  boat  of  course  rising  with  it,  ready  to 
proceed  on  her  way. 


Fig.  79. 

Thus,  let  A  B  and  C  D,  figure  79,  be  two  adjacent  levels  on  a 
canal ;  B  C  and  F  E  two  floodgates,  that  may  be  opened  and 
closed  at  pleasure.  Now,  suppose  a  boat  coming  up  the  canal 


was  required  to  make  a  cubic  inch  of  water  balance  or  counterpoise  a  cubic 
foot,  what  would  be  necessary  ?  169.  What  are  locks  in  canals  ?  Are  they 
used  in  a  level  country  ?  How  does  a  boat  ascend  through  a  lock  ?  Hovf 
does  the  boat  descend  ? 


HYDROSTATICS.  87 

at  D  is  to  pass  through  the  lock ;  the  gate,  F  E,  is  opened,  and 
the  boat  allowed  to  pass  in,  when  it  is  again  closed,  and  the 
water  let  in  through  small  gateways  in  the  large  floodgates 
B  C,  by  which  the  space  between  the  two  large  gates,  called 
the  lock,  is  soon  filled,  and  the  boat  raised  to  the  level  of  the 
water,  BA.  The  floodgate,  BC,  is  then  opened,  and  the  boat 
passes  onward.  It  is  evident  the  space  between  the  floodgates, 
or  the  length  of  the  lock,  cannot  be  less  than  the  length  of  the 
boats  made  to  pass  it. 

The  method  by  which  a  boat  is  made  to  pass  downward 
through  a  lock  will  now  be  understood  without  a  particular 
description. 

170.  When  water  is  conveyed  a  distance  for  the  purpose  of 
supplying  a  town,  it  is  sometimes  conducted  in  a  canal,  which 
may  be  covered  (as  is  the  Croton  aqueduct  in  New  York)  or 
open ;  but  often  close  pipes  are  used,  which  are  made  strong 
to  endure  great  pressure,  and  laid  a  little  below  the  surface, 
without  reference  to  its  unevenness.    But  it  is  to  be  noticed 
that  the  pipes  must  at  no  place  rise  higher  than  the  source 
from  which  the  water  proceeds.    In  this  way  water  may  be 
conveyed  even  to  the  upper  stories  of  houses,  provided  the 
source  is  sufficiently  elevated. 

171.  In  many  mechanical  operations  it  is  necessary  to  have 
some  convenient  means  for  finding  a  true  level,  or  horizontal 
line. 

For  this  purpose  a  vessel  of  water 
of  such  a  form  that  the  surface  may 
be  considerably  extended,  as  a  large 
basin,  will  answer  in  many  cases ; 
but  a  tube  bent  in  the  form  A  C  D  B, 
figure  80,  filled  with  water,  is  better. 
Fig.  so.  if  the  parts  A  C  and  B  D  are  of  the 

same  length,  when  it  is  perfectly  horizontal,  water  upon  being 
poured  in  will  rise  exactly  to  the  edge  at  both  ends  of  the  tube. 
To  determine  whether  a  beam,  or  floor,  or  other  object  is 
horizontal,  the  workman  has  only  to  place  the  instrument  upon 
it,  in  the  position  shown  in  the  figure,  and  fill  it  with  water. 
If  the  water  does  not  rise  exactly  to  the  edge  at  both  extremi- 
ties, he  of  course  knows  that  the  object  is  not  in  the  true  hori- 
zontal position.  If  he  wishes  to  determine  which  of  two  objects 
at  a  distance  from  each  other  is  highest,  he  places  it  upon  one 
of  them  in  a  horizontal  position,  and  sights  across  the  ends  of 
the  tube. 
The  above  explanation  exhibits  the  principle  of  the  instru- 

Quest.  170.  What  is  an  aqueduct  ?  May  an  aqueduct  be  open  like  a  canal, 
or  closed  ?  When  close  pipes  are  used,  why  may  not  the  aqueduct  be  carried 
to  any  place  higher  than  the  fountain?  171.  How  may  a  level  be  found  by 
means  of  a  basin  of  water  ?  How  by  means  of  a  bent  tube  ? 


88 


NATURAL     PHILOSOPHY. 


ment,  but  other  fixtures  are  usually  added  to  it  to  render  it 
more  convenient  for  use. 

172.  But  another  instrument,  called  a  spirit  level,  from  its 
compactness  and  little  liability  to  injury,  is  now  generally  used 
by  mechanics.     It  consists  of  a  cylindrical  glass  tube,  slightly 
curved,  and  filled  with  alcohol,  except  a  small  space  which 
contains  air,  and  is  sealed  by  closing  up  the  glass  at  each  end, 
In  whatever  position  it  is  placed,  the  air  will  be  uppermost  ; 
and  if  the  extremities  are  at  the  same  level,  it  will  be  in  the 
middle,  this  being  the  highest  point. 

If  the  tube  is  not  exactly 
level,  the  bubble  will  incline 
towards  the  highest  end.  Fi- 
gure  81  represents  the  tube 
inclosed  in  a  brass  case,  A  B, 

in  a  horizontal  position,  with  the  air-bubble  in  the  centre.  The 
tube  is  usually  inclosed  in  brass,  except  a  small  part  of  the 
upper  side. 

173.  Immersion  of  Solids  in  Liquids.  —  When  a  solid  is  im- 
mersed in  a  liquid,  it  is  evident  that  a  portion  of  the  liquid, 
equal  in  bulk  to  that  of  the  solid,  must  be  displaced,  else  it- 
would  be  possible  for  two  bodies  to  occupy  the  same  space  at 
the  same  time.    This  is  shown  very  easily  by  experiment  as 
follows  : 

Let  A  B  C  D,  figure  82,  be  a  vessel  with  per- 
pendicular  sides,  6  inches  square  at  the  bottom, 
and  a  foot  high,  partly  filled  with  water,  as  to 
the  figure  6.  As  it  is  just  6  inches  square  at 
the  bottom,  every  inch  in  height  will  contain 
just  36  cubic  inches  of  water;  2  inches  in 
height,  72  cubic  inches;  and  so  on.  Let  us 
suppose,  now,  a  block  of  marble,  or  other 
heavy  substance,  S,  precisely  4  inches  square, 
is  dr°PPed  mto  it;  5  a  portion  of  the  water  will 
be  displaced  or  moved  to  another  part  of  the 
vessel,  as  will  be  manifested  by  the  rise  of  the  surface  nearly 
to  the  figure  8,  just  as  if  so  much  more  liquid  had  been  poured 
in.  The  block,  S,  being  4  inches  square,  would  contain  just  64 
cubic  inches;  and  upon  measurement  after  its  immersion  in 
the  water,  the  surface  will  be  found  to  have  risen  1£  inches; 
showing  that  just  64  cubic  inches  of  water  had  been  displaced, 
for  36x1  £=64. 

Quest.  172.  How  is  the  spirit  level  constructed  ?  How  does  it  show  when 
a  true  level  or  horizontal  position  is  obtained  ?  173.  When  a  solid  is  totally 
immersed  in  a  liquid,  what  quantity  of  the  liquid  must  be  displaced  ?  How 
is  this  illustrated  by  figure  82  ?  If  the  vessel  is  6  inches  square,  and  a  cubical 
block  4  inches  on  each  side  be  dropped  into  it,  how  high  will  the  water  be 
made  to  rise  ? 


Fie  82 


HYDROSTATICS.  89 

174.  It  will  be  seen  that  we  have  here  an  excellent  method  to 
determine  exactly  the  bulk  or  solid  contents  of  an  irregular 
mass  of  any  solid  not  soluble  in  water;  for,  whatever  be  the 
form  of  the  mass,  it  will  always  displace  a  volume  of  water  just 
equal  to  itself;  and,  by  observing  the  rise  of  the  surface,  the 
additional  part  of  the  vessel  so  filled  can  be  at  once  calculated 
as  just  shown.    If,  for  instance,  an  irregular  mass  should  cause 
the  water  in  the  above  vessel  to  rise  just  2  inches,  we  should 
know  that  it  must  contain  72  cubic  inches;  and  so  of  any  other 
height. 

An  ingenious  practical  use  is  sometimes  made  of  this  pro- 
perty of  liquids  by  blacksmiths,  in  certain  cases  in  which  it  is 
necessary  to  use  a  given  weight  of  iron.  In  the  construction 
of  gun-barrels  for  government,  it  is  required  that,  when  finish- 
ed, they  should  have  a  prescribed  weight ;  and  in  order  to  this, 
to  prevent  great  waste,  it  is  necessary  for  the  workman  to 
commence  with  a  proper  quantity  of  iron.  The  iron  is  procured 
in  bars,  which,  however,  vary  a  little  in  size,  else  it  would  be 
sufficient  to  measure  the  same  length  of  the  bar  for  each  barrel. 
To  determine  the  proper  length,  whatever  may  be  the  size  of 
the  bar,  the  workman  proceeds  in  the  following  manner : 

He  first  procures  a  tub  of  the  proper  capacity,  as 
A  B,  figure  83,  and  fills  it  with  water  to  a  point,  P, 
which  is  to  be  ascertained  by  trial.  He  then  im- 
merses one  end  of  the  bar,  C  D,  perpendicularly, 
until  the  water  rises  so  as  just  to  fill  the  tub,  and 
marks  on  the  bar  the  line  to  which  it  is  wet ;  the  part 
immersed  will  then  be  just  sufficient  for  his  pur- 
pose. This  method  supposes,  as  will  be  seen  more 
fully  hereafter,  that  all  the  iron  used  is  of  equal 

Fig.  83.      densit7- 

175.  When  a  solid  is  immersed  in  a  liquid,  it  presses  down- 
ward with  a  force  equal  to  its  own  weight ;  and,  as  we  have 
seen,  when  wholly  immersed,  displaces  a  quantity  of  the  liquid 
equal  in  volume  to  itself.   If  this  quantity  of  the  liquid  is  lighter 
than  the  solid,  the  latter  will  sink,  but  if  heavier  it  will  swim. 
If  the  two  are  precisely  of  the  same  weight,  the  solid  will  re- 
main suspended  in  the  liquid,  in  whatever  position  it  may  be 
placed.    When  a  body  is  immersed  in  a  liquid  heavier  than 

Quest.  174.  How  may  we  determine  the  solid  contents  of  an  irregular 
mass  ?  Suppose  an  irregular  mass  should  cause  the  water  in  the  above  vessel 
to  rise  two  inches  when  immersed  in  it,  what  must  be  its  solid  contents  ? 
How  is  the  result  obtained  ?  How  does  the  blacksmith  determine  the  quan- 
tity of  iron  to  be  cut  from  a  bar,  in  the  manufacture  of  certain  articles,  as 
gun-barrels  ?  Does  this  method  suppose  all  the  iron  to  be  of  the  same  den- 
sity ?  175.  When  a  solid  is  immersed  in  a  liquid,  with  what  force  does  it 
press  downward  ?  When  wholly  immersed,  how  much  fluid  is  displaced  ? 
When  will  the  body  sink,  and  when  will  it  swim  ?  When  a  body  is  im- 


90 


NATURAL    PHILOSOPHY. 


Fig.  84. 


itself,  it  will  sink  until  it  displaces  a  quantity  of  the  liquid  just 
equal  in  weight  with  itself. 

176.  The  reason  of  the  above  statements  may  perhaps  be 
made  plainer  by  further  illustrations. 

Let  L  M,  figure  84,  be  a  vessel  filled 
with  water,  containing  a  cubic  block, 
A  B  C  D,  immersed  in  it,  which,  for  the 
present,  we  will  suppose  to  have  the 
same  weight  as  an  equal  bulk  of  water. 
It  is  evident  it  will  remain  exactly  in 
this  state  of  rest  unless  disturbed.  On 
the  upper  side  it  sustains  the  pressure 
of  the  column  of  water,  E  ADF,  which 
we  will  suppose  just  a  cubic  foot  also ; 
and  on  the  lower  surface,  B  C,  it  will  sustain  an  upward  pressure 
of  twice  this  amount,  since  the  depth  beneath  the  surface  is 
here  2  feet.  But  to  the  downward  pressure  of  one  cubic  foot 
of  water  is  to  be  added  its  own  weight  of  one  cubic  foot,  making 
it  just  equal  to  the  upward  pressure.  It  will  therefore  remain  at 
rest. 

177.  But  let  us  now  suppose  the  mass,  A  BCD,  is  heavier 
than  an  equal  volume  of  water ;  the  downward  and  upward 
pressure  of  the  water  will  be  the  same  as  before;  but  the  weight 
of  the  solid  being  greater  than  that  of  an  equal  volume  of  water, 
it  will  tend  to  sink  by  the  difference.    Again,  suppose  the  im- 
mersed body  to  be  lighter  than  water,  bulk  for  bulk,  it  is  easy 
to  see  that  the  solid  will  tend  to  rise  by  as  much  as  it  is  lighter 
than  an  equal  volume  of  water.    When  a  body  floats  in  water, 
the  absolute  weight  of  the  water  displaced  will  always  be  just 
equal  to  the  whole  weight  of  the  body. 

Let  LM,  figure  85,  be  a  cistern  of 
water,  and  A  B  C,  a  body  floating  in  it ; 
then  the  weight  of  the  water  displaced 
by  mnC  will  always  be  just  equal  to 
the  whole  weight  of  the  body,  ABC. 
For,  if  the  weight  of  the  water  displaced 
were  less  than  that  of  the  body,  it  would 
sink  lower,  and  displace  a  greater  quan- 
tity of  the  fluid ;  and  if  the  weight  of  the  water  were  greater 
than  that  of  the  body,  the  upward  pressure  of  the  surrounding 
water  would  be  greater  than  the  downward  pressure  of  the 


mersed  in  a  liquid  heavier  than  itself,  to  what  depth  will  it  sink  ?  176.  If  in 
figure  84,  the  block  A  B  C  D  is  of  the  same  weight  as  an  equal  volume  of 
water,  what  will  be  the  effect  ?  How  is  it  shown  that  it  would  remain  at  rest 
beneath  the  surface  ?  How  much  greater  is  the  upward  than  the  downward 
pressure  ?  Why  then  will  not  the  block  rise  to  the  surface  ?  177.  If  the 
block  were  heavier  than  an  equal  volume  of  water,  what  would  be  the  effect  ? 
If  lighter,  what  would  be  the  result  ?  When  a  body  floats  in  water,  how  will 
the  weight  of  the  water  displaced  compare  with  the  weight  of  the  body  ?  If  a 


HYDROSTATICS. 


91 


body,  and  it  would  rise ;  coming  to  a  state  of  rest  in  either  case, 
when  the  weight  of  the  displaced  fluid  is  just  equal  to  the  weight 
of  the  body. 

As  a  matter  of  course,  if  the  above  principles  are  correct,  no 
solid  can  float  on  the  surface  of  a  liquid,  if  it  be  heavier  than 
its  own  bulk  of  the  liquid;  but,  as  the  bulk  of  most  or  all  sub- 
stances can  be  increased  without  increasing  their  weight,  it 
may  be  formed,  however  heavy,  so  as  to  float.  Thus,  vessels 
made  of  brass,  iron,  and  other  heavy  substances,  readily  float 
upon  the  surface  of  water,  as  every  one  knows.  So  iron  steam- 
vessels  are  not  now  uncommon.  In  consequence  of  their  form, 
they  displace  just  as  much  water  as  if  they  were  solid ;  but  their 
weight  is  very  much  less.  If  they  are  filled  with  water,  therefore, 
they  immediately  sink. 

178.  The  effect  of  immersing  a  body  in  a  liquid  is  always  to 
lessen  its  apparent  weight,  as  every  one  has  noticed  who  has 
attempted  to  lift  a  stone  or  other  heavy  substance  in  water. 
In  the  water  it  is  perhaps  raised  without  difficulty;  but  on 
coming  to  the  surface,  a  great  and  sudden  increase  of  weight 
is  observed.  So  every  one  who,  while  bathing,  has  walked  in 
the  water,  has  observed  how  lightly  he  presses  upon  his  feet. 
If  the  depth  is  considerable,  and  the  body  is  immersed  to  the 
shoulders,  the  person  seems  to  himself  to  have  little  or  no 
weight ;  and,  if  there  is  even  a  moderate  current,  he  finds  him- 
self in  danger  of  being  washed  away,  in  consequence  of  the 
very  insecure  hold  his  feet  have  upon  the  bottom. 

179.  This  loss  of  weight  by 
a  body  when  immersed  in  a 
liquid,  as  may  be  inferred  from 
what  has  been  already  stated, 
is  always  just  equal  to  the 
weight  of  the  liquid  displaced 
by  it.  An  easy  method  of 
proving  this  important  prin- 
ciple is  as  follows.  Let  C, 
figure  86,  be  a  vessel  which 
we  will  at  first  suppose  empty, 
and  let  A  be  a  cylindrical  mass 
of  some  solid  capable  of  sink- 
ing in  water,  and  turned  very 
accurately  so  as  just  to  fit  in- 
side the  cylindrical  vessel,  D. 


Fig.  86. 


substance 'heavier  than  water,  bulk  for  bulk,  will  sink,  how  are  vessels  of 
iron  made  to  float  in  water  ?  178.  Why  does  a  body,  when  immersed  in 
water,  appear  to  be  lighter  than  in  the  air  ?  Why  is  it  that  a  person  wading 
in  deep  water  seems  to  himself  to  be  so  light  ?  Why  is  he  in  danger  of  being 
swept  away  if  there  is  a  current  ?  179.  What  is  the  loss  of  weight  of  a  heavy 
body,  when  immersed  in  a  liquid,  equal  to  ?  How  is  this  proved  by  the  use 
of  the  apparatus  represented  in  figure  86  ? 


92  NATURAL     PHILOSOPHY. 

Now  let  the  body,  A,  be  suspended  by  a  fine  thread  to  the  vessel, 
D,  and  an  exact  equipoise  produced  by  placing  weights  in  the 
scale-pan,  B.  Upon  pouring  water  in  the  vessel,  C,  the  scale- 
pan  B  will  preponderate ;  but  the  equipoise  will  be  again  re- 
stored by  filling  the  cylindrical  vessel  D  with  water.  Now,  as 
the  cylindrical  vessel  D  is  of  such  a  size  that  the  solid  mass  A 
will  exactly  fit  into  its  interior,  it  follows  that  the  water  with 
which  D  is  filled  is  precisely  equal  in  bulk  to  the  solid  A ; 
proving  that  the  apparent  loss  of  weight  suffered  by  A  on  be- 
ing immersed  in  water,  is  just  equal  to  the  weight  of  a  mass 
of  water  equal  in  bulk  to  itself. 

180.  If  a  body  lighter  than  water  be  first  sunk  by  means  of 
weights,  and  then  these  weights  removed,  it  will  rise  with  more 
or  less  force,  depending  upon  its  mass  and  its  weight  compared 
with  that  of  water.     Many  contrivances  on  this  principle  have 
been  suggested  for  raising  sunken  vessels,  and  for  lifting  vessels 
over  shoals  when  loaded  too  deeply  to  pass  without  assistance. 
A  machine  of  this  kind,  called  a  Camel,  in  use  in  several  places 
in  Europe,  consists  of  two  immense  boxes,  which  are  made 
water-tight,  and  filled  with  water,  and  then  lashed  strongly  one 
to  each  side  of  the  vessel,  below  the  surface  of  the  water.   The 
water  within  is  then  pumped  out,  and  their  buoyancy  is  suffi- 
cient often  to  raise  the  ship  several  feet. 

181.  Life-preservers  are  constructed  on  the  same  principle. 
They  are  made  of  some  flexible  substance,  as  India  rubber 
cloth,  and  of  such  a  form  as  usually  to  encircle  the  waist,  and 
be  easily  attached  to  the  body.    In  case  of  danger,  they  are 
readily  inflated  by  a  mouth-piece  and  valve  provided  for  the 
purpose,  and  are  then  so  light  and  buoyant  that  the  person  is 
in  no  danger  of  sinking.  Life-boats  are  also  constructed  on  this 
principle. 

182.  The  human  body  is  a  little  lighter  than  its  own  volume 
of  water,  and  of  course  ought  not  to  sink  entirely  beneath  the 
surface.     Usually,  it  is  found  that  about  half  the  head  will  float 
above  the  surface ;  and  with  presence  of  mind  and  the  proper 
exertion  of  the  hands  and  feet,  the  swimmer  finds  no  difficulty 
in  keeping  his  mouth  and  nose  above  the  water  so  as  to  breathe 
freely.     But  when  persons  unaccustomed  to  swimming  are 
accidentally  thrown  into  the  water,  not  having  sufficient  pre- 
sence of  mind,  or  not  knowing  how  to  move  the  limbs,  so  as 
to  bring  the  head  to  the  surface,  in  the  effort  to  breathe,  a 

Quest.  180.  What  will  be  the  effect  if  a  body  lighter  than  the  same  volume 
of  water  be  sunk  by  means  of  weights,  and  the  weights  afterwards  removed  ? 
What  is  the  design  of  the  machine  called  the  camel  ?  How  is  it  constructed  ? 
181.  How  are  life-preservers  constructed  ?  How  are  they  inflated  ?  182.  Is 
the  human  body  lighter  or  heavier  than  water,  bulk  for  bulk  ?  May  a  good 
swimmer  easily  keep  his  mouth  and  nose  above  the  water  ?  Why  is  it  that 


HYDROSTATICS.  93 

quantity  of  water  is  drawn  into  the  lungs,  by  which  the  weight 
of  the  body  is  so  increased  that  it  becomes  a  little  heavier  than 
an  equal  bulk  or  volume  of  water,  and  of  course  sinks  to  the 
bottom;  there  it  remains,  until,  by  its  decomposition,  the 
gases  that  are  formed  cause  it  to  expand  so  much,  that  it  dis- 
places more  water  than  is  equal  to  its  own  weight,  and  it  thus 
rises. 

The  bodies  of  fishes  are  very  nearly  of  the  same  weight  as  an 
equal  bulk  of  water ;  but  they  are  also  furnished  with  an  air- 
bladder,  by  means  of  which  they  are  able  to  change  the  bulk 
of  their  bodies,  and  therefore  rise  or  fall  at  pleasure.  The  air- 
bladder  is  usually  attached  to  the  spine  or  back-bone,  and  con- 
sists of  a  strong  muscular  sack  which  is  partly  filled  with  com- 
pressed air.  When  the  fish  wishes  to  descend,  the  muscles  of 
this  sack  are  tightly  drawn,  and  the  air  within  still  more  com- 
pressed, and  its  volume  diminished ;  but,  when  he  wishes  to 
rise,  these  muscles  are  relaxed,  and  the  air  within  expands, 
increasing  the  bulk  of  the  animal. 

183.  An  amusing  toy  is  sometimes  seen,  which 
consists  of  a  glass  jar  nearly  filled  with  water,  and 
having  several  glass  images  (C,  D  and  E,  figure  87) 
floating  in  it.  Over  the  top  is  tied  very  closely  a 
piece  of  bladder  or  leather ;  and  when  it  is  slightly 
pressed  with  the  hand,  the  images  are  seen  gradu- 
ally to  sink  to  the  bottom,  but  rise  again  as  soon 
as  the  pressure  is  removed.  The  images  are  made 
hollow,  and  contain  just  sufficient  air  to  make  them 
swim  under  the  ordinary  pressure  of  the  atmo- 
sphere; but,  when  the  pressure  is  increased  by 
placing  the  hand  upon  the  leather  covering  of  the 
jar,  the  volume  of  air  therein  is  diminished,  and 
water  forced  in  through  little  holes  in  the  feet. 
Fi  g?  Their  weight  is  then  so  increased  that  they  sink ; 
but,  on  the  removal  of  the  pressure,  the  air  within 
expands,  and  forces  out  a  portion  of  water,  and  the  image  again 
rises. 

184.  When  a  body  is  designed  to  float  in  a  liquid,  it  is  as  ne- 
cessary that  regard  should  be  paid  to  the  proper  support  of  its 
centre  of  gravity  (§  42)  as  if  it  were  intended  to  stand  perma- 
nently upon  a  plain,  otherwise  it  will  not  remain  in  its  proper 

persons  unaccustomed  to  swimming  almost  always  sink  in  a  short  time  when 
accidentally  falling  into  the  water?  What  is  said  of  the  weight  of  the  bodies 
of  fishes  as  compared  with  water  ?  By  what  means  do  they  manage  to  rise 
and  fall  at  pleasure  ?  183.  How  are  the  little  images  in  the  vessel  of  water, 
represented  in  figure  87,  made  to  rise  and  fall  in  the  water  ?  How  is  it  ex- 
plained ?  184.  Must  the  centre  of  gravity  of  a  body  floating  in  a  liquid  be 


94  NATURAL     PHILOSOPHY. 

position  in  the  liquid,  or  will  be  in  danger  of  being  capsized. 
But  the  various  circumstances  upon  which  the  stable  equili- 
brium of  a  body  floating  in  a  liquid  depends,  cannot  be  here 
investigated. 

185.  All  that  has  been  said  respecting  the  ascent  and  descent 
of  solids  in  liquids  applies  equally  to  two  or  more  liquids  in  the 
same  vessel.    If  the  liquids  are  incapable  of  acting  in  any  man- 
ner upon  each  other,  they  will  arrange  themselves  in  the  vessels, 
in  the  order  of  their  weights,  the  lighter  above  the  heavier. 
Thus,  oil  always  floats  upon  the  surface  of  water,  but  sinks  in 
alcohol.    If  a  bottle  with  a  small  neck  be  filled  with  water,  and 
the  mouth  inverted  in  a  vessel  of  alcohol,  the  water  will  be  seen 
to  form  a  descending  current  through  the  neck,  while  the  alco- 
hol, being  the  lighter  of  the  two,  will  gradually  rise  and  take 
its  place. 

Thus,  a  sailor  on  board  of  a  vessel  loaded  in  part  with 
brandy,  wishing  a  little  of  "the  ardent,"  filled  a  junk  bottle 
with  water,  and  holding  the  mouth  with  his  hand,  suddenly 
inverted  it  in  the  bunghole  of  a  cask,  filled  with  the  spirit.  After 
holding  it  there  some  time,  he  quickly  removed  it,  and 
found  it  filled  with  a  mixture  of  brandy  and  water,  just  suit- 
ed to  his  taste.  On  having  his  honesty  called  in  question,  he 
declared  he  had  done  no  injury  to  any  one,  as  he  left  the  cask 
as  full  as  he  found  it !  The  student  will  perceive,  that  though 
culpable  in  morals,  his  principles  of  philosophy  were  cor- 
rect. 

186.  Water,  when  heated,  expands,  and  therefore  becomes 
specifically  lighter,  and  as  a  necessary  consequence  rises  to  the 
surface.     Hence,  a  vessel  of  water  may  be  gradually  heated 
merely  by  having  a  tube  extend  from  it  to  the  fire,  though  it  be 
at  a  considerable  distance.   The  water  in  the  tube  is  first  heat- 
ed, and  ascends  to  the  boiler  or  vessel  to  which  the  tube  is 
connected ;  and,  at  the  same  time,  the  cold  water  in  the  vessel 
descends  in  the  tube,  and  is  in  its  turn  also  heated.   The  appa- 
ratus answers  better  if  there  are  two  tubes,  in  one  of  which 
the  cold  water  will  descend,  and  the  warm  water  ascend  in  the 
other. 

supported  ?  185.  If  two  liquids,  incapable  of  mixing  with  each  other,  are 
poured  into  a  vessel,  how  will  they  arrange  themselves  ?  Which  is  the 
heavier,  water  or  alcohol  ?  Why  does  oil  always  float  upon  the  surface  of 
water  ?  If  a  person  should  fill  a  bottle  with  water,  and  then  invert  it,  hold- 
ing the  mouth  in  alcohol,  what  would  be  the  result  ?  How  did  the  sailor 
obtain  a  quantity  of  brandy  from  a  cask  without  diminishing  the  quantity  of 
liquid  in  the  cask  ?  How  is  the  fact  to  be  explained  ?  186.  Why  does  water 
become  lighter  when  heated  ?  How  may  a  vessel  of  water  be  heated  by 
means  of  the  piece  of  apparatus  represented  in  figure  88  ? 


HYDROSTATICS, 


95 


Ml 


Let  A,  figure  88,  be  a  vessel  of 
water  supported  upon  a  stand  two 
or  more  feet  high,  and  let  C  D  be  a 
tube  extending  from  the  vessel,  A, 
to  the  flame  of  the  lamp,  L,  and  then 
doubling  and  returning,  the  two  ends 
being  carefully  soldered  into  the  bot- 
tom of  A.  By  the  lamp,  a  portion 
of  the  water  in  the  tube  is  heated, 
and  rises  in  the  part,  D,  a  current 
of  cold  water  at  the  same  time  de- 
scending in  C,  as  shown  by  the  ar- 
rows. In  this  way  a  cistern  of  water 
in  the  third  or  fourth  story  of  a 
building  is  often  kept  heated  by 
means  of  tubes  extending  from  it  to 
the  fire  in  the  kitchen  in  the  first 
story. 


Fig.  88. 


187.  Specific  Gravity.  —  By  the  specific  gravity  of  a  body  is 
meant  its  weight  when  compared  with  water,  which  is  adopted 
for  the  standard.     When,  therefore,  we  say  of  any  substance, 
that  its  specific  gravity  is  2  or  5,  we  mean  that,  bulk  for  bulk, 
that  substance  is  twice  or  five  times  as  heavy  as  water.  Thus, 
the  specific  gravity  of  sulphur  is  2 ;  since,  therefore,  a  cubic 
foot  of  water  weighs  62^  pounds,  a  cubic  foot  of  sulphur  would 
weigh  twice  as  much,  or  125  pounds.  When  we  say  the  specific 
gravity  of  gold  is  a  little  more  than  19,  we  mean  that  if  equal 
bulks  are  taken,  the  gold  will  weigh  a  little  more  than  19  times 
as  much  as  the  water. 

Water  has  been  agreed  upon  as  the  standard  of  comparison 
for  two  principal  reasons,  viz.  1st.  In  common  with  other  liquids, 
it  is  much  more  convenient  for  use  than  a  solid  would  be ;  and 
2d.  It  is  more  easily  and  cheaply  obtained  than  any  other 
liquid. 

188.  To  determine  the  specific  gravity  of  a  body,  all  that  is 
wanted  besides  its  own  weight  is  the  weight  of  a  quantity 
of  pure  water  of  precisely  equal  bulk  with  itself.     Thus,  if 
the  bulk  of  the  body  is  just  a  cubic  inch,  and  it  weighs  504 
grains,  and  we  know  the  weight  of  this  bulk  of  water  to  be  252 

Quest.  187.  What  is  meant  by  the  specific  gravity  of  a  body?  What  is 
meant  when  we  say  the  specific  gravity  of  a  body  is  2  or  5  ?  What  is  the 
weight  of  a  cubic  foot  of  water  ?  What  then  must  a  cubic  foot  of  sulphur 
weigh,  the  specific  gravity  of  which  is  2  ?  How  is  this  found  ?  Why  is 
water  taken  as  the  standard  of  specific  gravity  ?  188.  What  are  wanted  in 
order  to  determine  the  specific  gravity  of  a  body  ?  Having  the  weight  of  a 


96  NATURAL     PHILOSOPHY. 

grains,  it  is  of  course  just  twice  as  heavy  as  water ;  or,  in  other 
words,  water  being  assumed  as  our  standard,  and  its  specific 
gravity  calJed  1,  then  the  specific  gravity  of  the  body  in  ques- 
tion is  2.  Here,  it  will  be  seen,  we  have  divided  the  weight 
of  a  given  bulk  of  a  substance  by  the  weight  of  an  equal  bulk 
of  water,  and  the  quotient  we  call  the  specific  gravity  of  the 
body. 

189.  It  remains  then  only  to  devise  some  easy  method  to  find 
readily  the  weight  of  a  quantity  of  water  equal  in  volume  to 
any  substance,  the  specific  gravity  of  which  is  to  be  determined  ; 
and  this,  after  what  has  been  said  (§  176,  179,  and  180),  will  not 
be  difficult.    It  will  only  be  necessary  to  weigh  the  body  in  the 
air,  and  then,  when  suspended  by  a  fine  thread  or  hair,  in  water ; 
and  the  loss  of  weight  in  the  latter  case  will  be  the  weight  of 
a  quantity  of  water  equal  to  itself  in  bulk.  (§  178). 

190.  To  find  the  specific  gravity  of  a  solid  heavier  than  water, 
then,  first  weigh  it  in  the  air,  and  then,  when  suspended  by  a  fine 
thread  in  water,  subtract  its  weight  in  water  from  its  weight  in 
the  air,  and  divide  the  latter  by  the  difference,  and  the  quotient 
will  be  the  specific  gravity  required. 

Suppose  a  piece  of  copper  to  weigh  in  air  204.7  grains,  and  in 
water  181.7;  subtracting  the  latter  number  from  the  former,  we 
have  23  grains  for  its  loss  when  weighed  in  water.  Then 
dividing  204.7  by  23,  we  have  8.9,  which  is  the  specific  gravity 
of  the  copper. 

191.  If  the  body  is  so  light  as  to  swim  in  water,  this  method 
must  be  modified  a  little ;  but  the  details  cannot  be  given  here. 
So  also  if  the  substance,  the  specific  gravity  of  which  is  to  be 
determined,  is  in  the  state  of  powder,  or  is  soluble  in  water,  as 
common  salt  or  alum,  other  modifications  of  the  method  de- 
scribed above  must  be  devised,  which  are  fully  pointed  out  in 
larger  works  on  this  subject. 

A  balance  prepared  for  determining  the  specific  gravity  of 
bodies,  as  above  described,  is  called  a  hydrostatic  balance.  It 
differs  from  a  common  balance  only  in  having  the  scale-pans 
suspended  a  little  higher  from  the  table  to  admit  of  small  vessels 
of  water  being  placed  underneath,  and  also  in  having  hooks 
attached  to  the  under  side  of  the  scale-pans,  to  which  small 
substances  may  be  suspended  by  means  of  a  thread  or  horse- 
hair. 

That  the  results  may  be  accurate,  it  is  always  necessary  that 

body,  and  also  the  weight  of  an  equal  bulk  of  water,  how  is  the  specific 
gravity  of  the  body  obtained  ?  189.  Having  a  solid  body,  how  may  we  deter- 
mine the  weight  of  a  quantity  of  water  equal  to  it  in  volume  ?  190.  What  is 
the  rule  given  for  finding  the  specific  gravity  of  a  solid  ?  If  a  piece  of  copper 
weighs  in  the  air  204.7  grains,  and  in  water  181.7  grains,  what  will  be  its  spe- 
cific gravity  ?  191.  What  is  the  hydrostatic  balance?  Must  the  water  be 
pure  that  is  used  in  taking  specific  gravities  ? 


HYDROSTATICS.  97 

the  water  used  in  these  operations  should  be  perfectly  pure, 
and  also  of  the  proper  temperature,  which  is  usually  supposed 
to  be  60°  Fahrenheit. 

192.  The  specific  gravity  of  a  liquid  may  be  readily  deter- 
mined in  several  ways,  one  or  two  of  which  will  be  mentioned. 
Let  a  phial  with  a  small  mouth  be  accurately  balanced  with 
weights,  and  then  filled  with  pure  water,  and  its  weight  ascer- 
tained.   Then  fill  it  with  the  liquid  under  examination,  and 
again  weigh  it ;  and  divide  the  weight  of  the  latter  liquid  by 
the  weight  of  the  water,  and  the  quotient  will  be  the  specific 
gravity  of  the  liquid  as  required. 

Suppose  a  bottle  to  be  first  accurately  balanced  in  the  scales 
by  a  weight,  and  then  when  filled  with  water  to  weigh  625 
grains,  but  when  emptied  and  again  filled  with  diluted  sul- 
phuric acid,  to  weigh  1000  grains;  it  is  plain  we  have  by  this 
means  the  weight  of  equal  volumes  of  the  two  liquids,  and  to 
obtain  the  specific  gravity  of  the  acid  we  have  only  to  divide 
its  weight  (1000  grains)  by  the  weight  of  the  water  (625  grains,) 
Thus,  1000-^625=1.6,  which  is  the  specific  gravity  of  the  acid. 
In  like  manner,  if,  when  emptied  and  again  filled  with  alcohol, 
it  should  be  found  to  weigh  537.5  grains ;  then,  537.5-^625= 
0.860,  which  is  the  specific  gravity  of  the  alcohol.  If  the  bottle 
were  made  of  such  a  size  that  it  would  hold  precisely  1000 
grains  of  water,  then  the  weight  of  any  other  liquid  contained 
in  it  when  filled,  divided  by  1000,  would  be  the  specific  gravity 
of  that  liquid.  Thus,  if  such  a  bottle  would  hold  1600  grains 
of  diluted  sulphuric  acid,  then  its  specific  gravity  would  be 
1600-^  1000= 1.6.  (See  Author's  Chemistry,  page  113.) 

193.  An  instrument  called  a  hydrometer  is  also  used  for  this 
purpose.    We  have  seen  (§  179)  that  when  a  body  is  immersed 
in  a  liquid  heavier  than  itself,  it  sinks  until  it  displaces  a  quan- 
tity of  the  liquid  equal  to  itself  in  weight.     The  same  solid, 
therefore,  must  sink  deeper  in  liquids  that  are  light  than  in 
those  that  are  heavier;  and  by  having  the  solid  of  a  convenient 
form  and  properly  marked,  in  accordance  with  the  results  of 
previous  trials,  the  depth  to  which  it  sinks  in  any  liquid  may 
be  made  to  indicate  with  considerable  accuracy  the  specific 
gravity  of  that  liquid. 

Quest.  192.  What  is  the  first  method  mentioned  for  finding  the  specific 
gravity  of  a  liquid?  If  the  bottle  were  made  so  as  to  hold  just  1000  grains 
of  water,  what  only  would  be  necessary  in  obtaining  the  specific  gravity  of  a 
liquid  ?  193.  What  is  the  design  of  the  hydrometer  ?  How  is  it  used  ?  Why 
does  it  sink  deeper  in  a  light  liquid  than  in  a  heavy  one  ?  How  is  the  hydro- 
meter constructed  ?  Why  is  it  loaded  with  mercury  or  shot  ?  How  is  the 
specific  gravity  of  a  liquid  shown  by  the  hydrometer  ?  If  two  columns  of 
liquids  of  different  specific  gravities  are  made  to  balance  each  other  in  the 
upright  parts  of  a  tube  bent  in  the  form  represented  in  figure  90,  what  will 

9 


: 


.      :- 


100  NATURAL     PHILOSOPHY. 

mixture  sold  for  the  pure  article ;  but,  by  testing  the  specific 
gravity,  the  imposition  can  usually  be  detected.  The  lactometer, 
for  determining  the  purity  of  milk,  and  the  oleometer,  for  ascer- 
taining the  purity  of  oil,  are  only  modifications  of  the  hydrome- 
ter (5 193)  to  adapt  them  to  their  specific  purposes. 

196.  The  specific  gravity  of  a  gas  may  be  determined  in  the 
same  manner  as  described  above  (§ 192)  for  obtaining  that  of  a 
liquid ;  but,  in  consequence  of  the  extreme  lightness  of  these 
substances,  atmospheric  air  is  usually  assumed  as  the  standard 
to  which  they  are  referred,  in  order  to  avoid  the  fractions  that 
would  otherwise  embarrass  our  operations.     Let  a  flask  of 
suitable  size  be  provided  with  a  good  faucet  and  then  weighed, 
first  when  filled  with  air,  and  then  after  being  exhausted  of  air 
by  means  of  the  air-pump.  The  difference  will  show  the  weight 
of  the  air  it  contained.     Then,  let  it  be  filled  with  the  gas  in 
question,  and  again  weighed,  and  from  this  subtract  the  weight 
of  the  flask,  and  we  have  the  weight  of  the  gas  that  was  in  it. 
Divide  this  last  by  the  weight  of  the  air  first  obtained,  and  the 
quotient  will  be  the  specific  gravity  of  the  gas,  as  required. 
Let  us  suppose  we  have  a  flask  fitted  with  a  suitable  faucet, 
which  will  contain  just  28  grains  of  atmospheric  air,  but  only 
27  grains  of  nitrogen  gas.  Then,  27-i-28=. 964,  which  is  nearly 
the  proper  specific  gravity  of  this  substance.   (For  further  re- 
marks on  this  subject,  see  Author's  Chemistry,  page  1 1 3.) 

197.  Motions  of  Liquids. — This  branch  of  Hydrostatics,  which 
treats  of  liquids  in  motion,  has  sometimes  been  called  Hydrau- 
lics, in  contradistinction  from  Hydro-dynamics,  which  treats 
only  of  the  laws  which  prevail  in  liquids  when  at  rest. 

198.  When  a  small  hole  is  made  in  the  side  of  a  vessel  filled 
with  a  liquid,  a  stream  is  seen  to  issue  from  it  with  more  or 
less  velocity,  depending  upon  circumstances  which  are  now  to 
be  noticed.   The  force  that  puts  the  liquid  in  motion  must,  before 
the  orifice  was  made,  have  caused  a  constant  pressure  against 
the  portion  of  the  vessel  removed ;  in  other  words,  it  is  the 
general  pressure  of  the  liquid.    This  pressure  we  know  to  be 
proportional  to  the  perpendicular  depth  below  the  surface  of 
the  liquid  (§  158) ;  and  we  may  here  infer  that  the  lower  the 
orifice  is  below  the  level  of  the  liquid,  the  greater  will  be  the 
violence  with  which  the  liquid  will  issue. 

lactometer?  What  is  an  oleometer?  196.  What  is  made  the  standard  of 
specific  gravity  for  the  gases  ?  Will  a  flask  weigh  less  when  exhausted  than 
when  filled  with  air  ?  How  is  the  specific  gravity  of  a  gas  found  ?  If  a  flask 
is  capable  of  holding  28  grains  of  air,  but  only  27  grains  of  nitrogen,  what 
must  be  the  specific  gravity  of  this  gas  ?  197.  Of  what  does  the  branch  of 
science  called  Hydraulics  treat?  198.  Why  does  the  water  rush  from  a 
vessel  filled  with  water  when  a  hole  is  made  in  the  side  ?  Must  there  have 
been  a  constant  pressure  against  the  part  before  the  hole  was  made  ?  To 
what  is  this  pressure  proportional  ? 


H  Y  DROST  A  Tit!  3.    ; 

199.  It  is  found  by  experiment  that  the  quantities  of  liquid 
which  escape  from  orifices  of  the  same  size  at  different  depths, 
other  things  being  the  same,  are  as  the  square  roots  of  these 
depths. 

Thus,  let  A  B  C  D,  figure  91,  be  a  vessel  with 
perpendicular  sides,  filled  with  water,  having 
orifices  of  the  same  size  at  E,  one  foot  below 
the  surface;  at  F,  four  feet;  and  D,  nine  feet 
below  the  surface ;  and  let  it  be  supposed  that 
the  vessel  is  all  the  time  kept  quite  full  by  pour- 
ing in  water  at  the  top  as  it  issues  from  the 
orifices  below.  Then,  it  is  found  by  accurate 
experiment,  that,  in  a  given  time,  as  a  minute, 
twice  as  much  water  will  escape  at  F  as  at  E ; 
and  at  D,  three  times  as  much.  But  2  is  the 
square  root  of  4,  and  3  the  square  root  of  9; 
therefore,  as  above  stated,  the  quantities  of 
Fi  Q1  water  discharged  at  the  different  orifices  are 

as  the  square  roots  of  the  distances  respectively 
beneath  the  surface.  Now,  as  the  orifices  are  all  of  the  same 
size,  it  is  plain  that  the  velocities  of  the  several  streams  must 
be  exactly  proportional  to  the  quantities  of  water  issuing  in  a 
given  time.  Thus,  the  velocity  of  the  stream  from  F  will  be 
twice  that  of  the  stream  from  E,  &c.  To  obtain  a  fourfold 
quantity  of  water,  and  therefore  a  fourfold  velocity,  the  orifice 
would  have  to  be  made  16  feet  below  the  surface ;  and  to  pro- 
duce a  fivefold  velocity,  it  must  be  25  feet  beneath  the  surface, 
and  so  on. 

It  has  been  heretofore  seen  (§  78)  that  when  a  heavy  body  falls  a  given 
distance,  as  a  foot  in  a  second,  it  always  acquires  at  the  end  of  the  time  a 
velocity  of  2  feet  a  second  ;  and  if  it  continue  to  fall  2  seconds,  it  will  pass 
through  4  feet,  and  acquire  a  velocity  of  4  feet  a  second.  At  the  end  of 
another  second,  it  would  be  9  feet  from  its  starting  point,  and  would  have 
a  velocity  of  6  feet  a  second  ;  and  so  on. 

It  appears,  then,  that  a  heavy  body  in  falling  a  given  distance,  as  a  foot, 
acquires  a  certain  velocity ;  and  that  in  order  to  double  this  velocity,  it 
must  fall  4  times  the  first  distance,  or  4  feet ;  and  to  triple  its  velocity,  it 
must  fall  9  times  the  first  distance,  or  9  feet. 


Quest.  199.  If  several  orifices  are  made  at  different  depths,  what  will  be  the 
proportion  of  the  several  quantities  of  water  discharged  from  them  ?  If  these 
orifices  are  made  at  the  depth  of  1,  4,  and  9  feet  beneath  the  surface,  what 
will  be  the  relative  quantities  of  water  discharged  ?  As  the  orifices  are  of 
the  same  size,  must  the  velocity  of  the  several  currents  be  in  the  same  ratio 
as  the  quantities  discharged  ?  To  obtain  a  fourfold  velocity,  what  must  the 
depth  be  ?  What  to  obtain  a  fivefold  velocity  ?  If  a  heavy  body  should  fall  a 
foot  in  a  second,  what  will  be  its  final  velocity  ?  How  far  must  it  fall  to  acquire 
twice  this  velocity  ?  How  far  to  acquire  six  times  the  velocity  it  had  at  the 
end  of  the  first  second  ?  Will  the  velocity  with  which  a  liquid  issues  from  an 


102  i%i,..*  JNA  T  VRA.L     PHILOSOPHY. 

*  ».{'  -t  *•  2  *     *  •«  .       ^   +*    '"-•*. 

It  will  therefore-  be  evident  that  the  velocity  with  which  & 
liquid  issues  from  an  orifice  will  be  the  same  as  a  heavy  body 
would  acquire  in  falling  the  distance  from  the  surface  of  the 
liquid  to  the  orifice. 

If  two  vessels  precisely  alike,  with  similar  orifices  at  the 
bottom,  are  filled  with  water,  and  one  is  allowed  to  empty 
itself,  but  the  other  kept  constantly  full  by  the  addition  of  fresh 
fluid,  when  the  water  is  all  discharged  from  the  former,  it  will 
be  found  that  just  twice  as  much  has  escaped  from  the  latter 
as  from  the  former. 

This,  it  will  be  perceived,  is  a  necessary  result  from  the  prin- 
ciples above  developed,  in  connection  with  the  law  that  a  falling 
body  in  any  given  time  traverses  just  half  the  distance  it  would 
pass  through  in  the  same  time,  if  moving  uniformly  with  its 
final  velocity.  (5  77.) 

200.  It  follows  from  these  principles 
«v  also,  that  if  an  orifice  is  made  upward, 
|  the  issuing  jet  should  rise  just  as  high  as 
the  surface ;  since  a  body  projected  per- 
pendicularly upward  will  rise  precisely  to 
the  same  height  as  the  distance  it  would 
have  fallen  by  the  force  of  gravity  in  the 
same  time.  Let  A  B,  figure  92,  be  a  cistern 
of  water,  with  tubes  at  different  distances 
beneath  the  surface,  having  their  mouths 
bent  upward,  as  E,  D,  and  C ;  then  the  jets 
issuing  from  them  should  rise  just  to  the 
surface  of  the  water.  But  this  is  found  not 
to  be  precisely  the  case  when  the  experi- 
ment is  made,  as  the  liquid  is  considerably 
retarded  by  friction  against  the  sides  of 
the  orifice,  and  by  the  resistance  of  the 
air. 

201.  The  jet  of  7  inches  diameter  from  the  inverted  syphon 
through  which  the  water  of  the  Croton  aqueduct  at  present 
crosses  under  Harlem  River,  9  miles  from  the  city  of  New 
York,  affords  probably  as  good  an  opportunity  to  make  the 
experiment  on  a  large  scale  as  there  is  in  the  world.  The 
orifice,  according  to  Mr.  Tower,  is  120  feet  below  the  surface 
of  the  water  in  the  aqueduct  on  the  bank  of  the  river  above; 
but  the  water  rises  in  the  jet  only  about  115  feet. 

orifice  be  equal  to  that  a  heavy  body  would  acquire  in  falling  from  the  surface 
to  the  orifice  ?  200.  If  an  orifice  open  upward,  how  high  should  the  jet  rise  ? 
How  is  figure  92  to  be  explained  ?  Why  will  not  the  water  rise  as  high  as 
the  surface  of  the  reservoir  ?  201.  In  the  jet  from  the  inverted  syphon  con- 
nected  with  the  Croton  aqueduct,  how  high  does  the  water  rise  ?  What  is 
the  height  of  the  water  above  the  orifice  ? 


Fig.  92, 


HYDROSTATICS.  103 


202.  The  distance  to  which  water 
will  spout  from  horizontal  jets,  at 
different  depths  below  the  surface, 
will  be  greatest  in  those  which  are 
midway  between  the  top  and  bot- 
tom. Thus,  a  jet  from  D,  figure  93, 
will  strike  the  ground  at  a  greater 
distance  from  the  cistern  A  B,  than 
one  issuing  either  from  C  or  E. 


Fig.  93. 


203.  The  quantity  of  water  that  will  be  discharged  from  an 
orifice  in  a  given  time  depends  considerably  upon  the  nature 
of  the  orifice.    Thus,  if  an  aperture  of  a  given  size  be  made  in 
a  vessel  of  sheet-iron,  it  is  found  it  will  not  discharge  as  much 
water  as  if  the  sides  were  thicker ;  or,  which  is  still  better, 
if  a  short  tube  were  inserted  just  even  with  the  inner  surface 
of  the  vessel.     The  reason  of  the  difference  is  no  doubt  to  be 
attributed  to  the  partially  opposing  cross-currents  that  are 
more  liable  to  be  found  in  the  case  of  a  vessel  with  thin  sides 
and  without  a  tube.    Different  modifications  of  the  pipe,  not 
here  detailed,  have  peculiar  effects  in  increasing  or  diminishing 
the  flow  of  the  water. 

204.  The  above  remarks  apply  only  to  pipes  of  very  moderate 
length  in  proportion  to  their  diameter ;  the  effect  of  long  pipes 
is  always  to  retard  the  flow  of  water  by  reason  of  the  friction 
against  their  sides.    And  this  retardation  by  friction  is  propor- 
tionally greater  in  small  pipes  than  in  large  ones,  so  that  a  pipe 
2  inches  in  diameter  will  discharge  in  a  given  time  5  times  as 
much  water  as  one  only  1  inch  in  diameter.    Were  it  not  for 
the  greater  friction,  proportionally,  of  the  small  pipe,  the  larger 
would  discharge  only  4  times  as  much  as  the  smaller ;  or,  the 
quantities  discharged  would  be  proportional  to  the  areas  of 
their  sections. 

205.  Water  in  rivers  and  canals  is  much  retarded  in  its 
course  by  friction  against  the  bottom  and  sides,  so  that  the  mo- 
tion is  much  the  most  rapid  at  the  surface  and  in  the  middle  of 
the  stream.    The  resistance  is  also  very  much  increased  by  the 
great  unevenness  of  the  surface  over  which  the  water  glides, 
and  by  obstacles,  as  stones  and  other  heavy  bodies  lying  at  the 

Quest.  202.  If  several  orifices  are  made  in  the  side  of  a  vessel  filled  with 
water,  from  which  will  the  water  jet  farthest  ?  203.  Does  the  quantity  of 
water  that  escapes  from  an  orifice  depend  upon  its  nature  ?  How  does  a 
short  tube  affect  the  discharge  ?  What  reason  is  given  ?  204.  To  what 
pipes  only  does  the  explanation  apply  ?  Is  there  any  friction  between  liquids 
and  solids  ?  How  much  more  water  will  a  pipe  2  inches  in  diameter  discharge 
than  a  tube  only  1  inch  in  diameter  ?  205.  Is  water  retarded  in  rivers  and 


104  NATURAL     PHILOSOPHY. 

bottom ;  so  that  the  velocity  of  water  in  rivers  is  always  greatly 
less  than  it  otherwise  would  be.  It  has  been  found  by  calcula- 
tion that  the  water  of  the  river  Rhone  in  Europe,  but  for  the 
resistance  it  meets  with  in  its  course,  ought  to  have  a  velocity 
of  about  170  miles  per  hour  before  reaching  the  ocean,  whereas 
its  real  velocity  is  only  4  or  5  miles  an  hour. 

Sudden  turns  in  the  course  of  pipes  conveying  water,  and 
in  the  course  of  rivers,  operate  also  to  retard  the  water  very 
much. 

206.  A  solid  in  motion  through  a  liquid  meets  with  much 
resistance  from  it,  proportional  to  its  size  and  form.  A  piece 
of  board,  it  is  well  known,  requires  much  more  force  to  move 
it  through  water  when  its  flat  side  is  presented  in  the  direc- 
tion of  its  motion,  than  when  it  is  moved  in  the  direction  of  its 
edge. 

The  oarsman  in  plying  his  boat  always  keeps  the  flat  surface 
of  the  blade  of  his  oar  in  the  direction  in  which  he  pulls ;  but 
on  removing  his  oar  from  the  water  he  presents  the  edge  in 
the  direction  in  which  it  is  to  move. 

The  sailing  of  a  ship  depends  much  upon  her  form,  on  ac- 
count of  the  resistance  of  the  water;  and  great  effort  has  been 
made  to  determine  the  form  in  which  this  resistance  shall  be 
the  least  possible.  To  attain  this  object,  it  is  found  that  regard 
must  be  had  to  the  shape,  not  only  of  the  forward  part  or  bow 
of  the  ship,  which  is  presented  in  the  direction  of  her  motion, 
but  also  to  that  of  her  stern.  This  must  be  of  such  a  form  that 
the  water  may  readily  and  freely  close  around  her  as  she 
glides  through  it,  else  a  great  depression  of  the  surface  will  be 
observed  immediately  behind  her,  below  the  common  level,  in 
consequence  of  which  much  of  the  propelling  force,  whether  it 
be  wind  or  steam  power,  will  be  lost.  The  resistance  of  the 
water  to  a  vessel  moving  through  it  increases  rapidly  with  the 
speed.  If  it  requires  a  certain  force  to  propel  a  ship  5  miles  an 
hour,  it  requires  much  more  than  double  the  force  to  propel 
her  at  double  this  speed ;  and  so  of  any  other  proportion. 

The  forms  of  the  bodies  of  fishes  and  birds  are  found  upon 
examination  to  be  admirably  adapted  by  nature  to  facilitate 
their  movements  through  the  fluids  which  constitute  their  pro- 
per elements. 

canals  ?  Is  the  motion  of  the  water  most  rapid  at  the  top  or  bottom  ?  What 
would  be  the  velocity  of  the  water  in  the  river  Rhone  in  Europe,  on  reaching 
the  sea,  if  it  was  not  retarded  in  its  course  ?  What  is  its  actual  velocity  ? 
206.  In  what  direction  may  a  piece  of  board  be  moved  through  the  water 
with  the  least  resistance  ?  Does  the  sailing  of  a  ship  depend  upon  her  form  ? 
Must  regard  be  paid  to  the  form  of  her  stern,  as  well  as  to  the  form  of  her 
bow  ?  What  must  be  the  form  of  a  ship's  stern,  in  order  that  she  may  sail 
well  ?  Does  the  resistance  increase  with  the  speed  ?  Are  fishes  fitted  for 
gliding  easily  through  the  water  ? 


HYDROSTATICS. 


105 


207.  Hydraulic  Machines. — Water  has  been  used  as  a  power  for  pro- 
pelling machinery  from  a  very  early  period.  For  this  purpose  it  is  used 
in  two  modes,  either  by  causing  it  to  act  simply  by  its  weight  on  the 
circumference  of  a  wheel,  or  by  the  impulse  of  its  motion  when  issuing 
from  under  strong  pressure.  The  motion  is  then  transmitted  in  the  usual 
manner,  by  wheel-work  or  other  contrivances,  to  the  machinery  which  it 
is  required  to  move.  Sometimes  these  two  modes  are  combined. 

208.  In  the  case  of  the  breast- 
wheel,  the  water  acts  in  the  former 
of  the  two  modes  above  described 
Figure  94  represents  a  section  of 
this  wheel  perpendicular  to  the  axis. 
This  wheel  is  constructed  with  fixed 
boxes  or  buckets,  which  on  one  side 
are  more  or  less  erect  in  their  posi- 
tion, and  therefore  capable  of  retain- 
ing the  water,  which  acts  by  its 
weight,  and  turns  the  wheel,  until, 
approaching  the  lowest  point,  they 
are,  one  after  another,  emptied,  and 


Fig.  94. 


ascend  in  an  inverted  position  on  the  opposite  side.  It  is  of  course  advan- 
tageous to  cause  the  water  to  fall  upon  the  wheel  as  near  the  top  as  may 
be,  in  order  to  fill  as  many  of  the  buckets  as  possible;  but  sometimes  it  is 
made  to  strike  the  wheel  very  low,  even  below  a  line  horizontal  with  its 
axis.  But,  in  this  case,  it  is  usually  made  to  act  also  by  its  momentum 
acquired  in  issuing  from  the  reservoir  or  dam  above. 

209.  The  undershot-wheel,  which 
is  represented  in  figure  95,  is  an 
ordinary  wheel  turning  on  an  axis, 
and  furnished  with  a  number  of  flat 
boards  placed  at  equal  distances  on 
its  rim,  so  as  to  project  from  it  in 
directions  nearly  diverging  from  its 
centre,  and  having  their  flat  faces 
of  course  nearly  at  right  angles  to 
the  direction  of  the  stream.  These 
are  called  float-boards.  The  wheel 
Fig.  95.  is  then  so  placed  that  its  lower  edge 

is  immersed  in  the  stream,  called 

ihe  mill-course ;  and  the  current  of  water  acting  against  the  float-boards 
by  its  momeYitum  causes  it  to  revolve  in  the  direction  of  the  stream.  The 
water  may  be  allowed  to  issue  over  the  top  of  the  reservoir  by  a  sluice- 
way, as  shown  in  the  figure,  and  strike  the  wheel  by  the  momentum  ac- 
quired in  its  fall ;  or  the  perpendicular  wall  of  the  reservoir  may  be  placed 
aear  to  the  wheel,  and  the  water  allowed  to  escape  by  a  gate-way  at  the 
bottom,  nearly  on  a  level  with  the  bottom  of  the  wheel.  The  velocity  given 
it  in  this  case  by  the  pressure  of  the  "  head  of  water"  above  will  be  the 
same  (§199)  as  will  be  acquired  in  the  preceding  case  by  its  descent. 

Quest.  207.  Has  water  been  long  used  for  propelling  machinery  ?  In  what 
two  ways  is  it  made  to  act  ?  208.  How  does  it  act  in  the  case  of  the  breast- 
wheel  ?  How  is  it  constructed  ?  209.  How  is  the  undershot-wheel  turned  ? 
Why  is  this  name  applied  to  it  ? 


106 


NATURAL     PHILOSOPHY. 


This  kind  of  wheel  is  sometimes  called  a  tide,  or  stream-wheel,  and  is 

said  to  be  the  oldest  construction  in  use. 

210.  The  kind  of  water-wheel  repre- 
sented in  figure  96,  is  called  an  overshot 
wheel.  Like  the  breast-wheel,  on  its  rim 
a  number  of  buckets  are  constructed  to 
contain  water,  which  acts  by  its  weight, 
precisely  as  in  the  breast-wheel,  to  turn 
it ;  but,  as  the  water  is  let  on  quite  at  the 
top  by  a  flume,  A  B,  more  of  the  buckets 
will  at  any  time  while  in  motion  be  filled. 
If  the  water  has  considerable  momentum 
when  let  on  the  wheel,  this  also  assists  in 
.  (  giving  it  motion.  This  wheel,  though 

very  effective,  has  the  disadvantage  of 

requiring  for  its  use  a  waterfall  of  considerable  height. 

211.  A  water-wheel  called  the  tub-wheel  is  much  used  in  flouring  and 
other  mills  in  this  country.    It  receives  its  name  from  the  fact  that  it  con- 
sists of  a  large  tub  without  a  bottom,  in  the  inside  of  which,  on  the  arms, 
the  float-boards  are  placed,  the  wheel  being  in  a  horizontal  position,  and 
having  the  shaft  perpendicular.    The  water  is  conveyed  to  the  wheel  by  a 
proper  flume  or  sluice-way,  and  acts  solely  by  its  impulse. 

212.  Most  machines  used  for  raising  water  at  the  present  day,  act  in 
part  at  least  by  atmospheric  pressure,  and  will  therefore  be  considered  in 
the  Chapter  on  Pneumatics  ;  but  one  or  two  will  claim  to  be  noticed  here. 

The  cochleon,  or  screw  of  Archimedes,  seems  to  have  been 
one  of  the  earliest  inventions  of  man  for  this  purpose.  It  con- 
sists of  a  tube  wound  around  in  the  form  of  a  spiral,  and 
placed  in  an  inclined  position,  as  represented  in  figure  97. 

The  inclination  must 
be  so  great  that  the 
parts  B,  D,  F,  H,  K, 
shall  be  lower  than  the 
parts  A,  C,  E,  &c.  If, 
therefore,  portions  of 
liquid  are  contained 
at  the  former  points, 
it  will  not  escape,  since 
these  parts  of  the  tube 
constitute  dish-like  ca- 
vities capable  of  re- 

pi    9  taining  it.  Let  us  sup- 

pose the  tube  fixed  on 

an  axis  now  to  be  turned  as  if  to  screw  it  down,  while  the 
lower  end  is  immersed  in  water ;  a  portion  will  enter  at  A  and 
pass  on  to  B  as  down  an  inclined  plane.  But  as  it  turns,  the 

Quest.  210.  How  is  the  overshot-wheel  constructed  ?  How  does  the  water 
act  upon  this  wheel?  What  disadvantage  has  this  wheel  ?  211.  Howisthetaft- 
wlieel  constructed  ?  212.  In  what  chapter  are  the  different  kinds  of  pumps 
described  ?  What  is  the  cochleon  or  screw  of  Archimedes  ?  How  is  the 


A. 


HYDROSTATICS.  107 

part  B,  keeping  its  same  position  with  reference  to  the  water 
contained  in  its  cavity,  will  gradually  rise  to  c,  and  so  on  to 
D,  while  another  whirl  of  the  spiral  will  take  its  place  at  B. 
Thus,  a  portion  of  water  will  be  carried  or  up-screwed,  up — 
we  may  say — quite  to  the  top,  to  be  there  discharged.  At  the 
same  time,  other  portions  will  be  ascending  in  the  several 

whirls  of  the  spiral,  each  in 
turn  delivering  its  portion  of 
the  fluid.  As  before  intimated, 
it  is  necessary  that  the  whole 
should  be  so  much  inclined 
that  there  shall  be  a  descent 
from  A  to  B,  from  C  to  D,  &c., 
so  as  to  form  cavities  for  con- 
taining portions  of  water. 

213.  The  centrifugal  pump  is  an 
instrument   for   raising   water   by 
means  of  the  centrifugal  force  which 
is  given  to  a  column  of  it.  Let  A  B, 
figure  98,*  be  a  solid  piece  of  tim- 
ber, and  C  D   a  tube  attached  to 
arms  projecting  from  it;  and  let 
__  the  whole  stand  in  water  supported 
g  upon  a  pivot  on  which  it  may  turn. 
_==^  If  it  is  now  made  to  turn  rapidly, 
such  a   centrifugal   force  will   be 
given  to  the  column  of  water  in  the 
Fig- 98.  tube  CD,  that  it  will   be  thrown 

from  the  mouth  D  in  every  direction  with  great  violence. 

water  raised  by  means  of  it  ?  Why  must  it  be  placed  in  an  inclined  po- 
sition ?  213.  What  is  the  centrifugal  pump  ?  How  is  it  worked  ? 

*  Ewbank's  Hydraulics,  page  230. 


108  NATURAL     PHILOSOPHY. 


CHAPTER  III. 


PNEUMATICS. 

214.  THE  earth  is  constantly  surrounded  by  a  great  mass 
of  gaseous  matter,  called  the  atmosphere  or  atmospheric  air, 
which  extends  a  considerable  distance  above  its  surface.    Its 
presence,  when  it  is  perfectly  at  rest,  is  scarcely  perceptible ; 
but,  if  we  attempt  to  move  the  hand  or  a  fan  rapidly  through 
it,  it  manifests  itself  by  its  resistance,  and  by  the  motion  which 
is  communicated  to  it.     It  obeys  laws  very  similar  to  those 
treated  of  in  the  preceding  Chapter,  but  not  precisely  the 
same,  as  air  is  considered  perfectly  elastic. 

The  various  other  gases,  besides  atmospheric  air,  have  the 
same  mechanical  properties;  and  the  remarks  made  in  this 
chapter  concerning  atmospheric  air  may,  in  general,  be  con- 
sidered as  applying  equally  to  them. 

215.  Air  is  a  material  substance,  and  possesses  all  the  pro- 
perties of  matter,  as  impenetrability  (\  9),  weight,  inertia,  &c. 
It  has  also  a  very  feeble  blue  colour,  as  is  evident  from  its 
causing  distant  hills  and  mountains  to  appear  of  this  colour. 
Other  gases  also  possess  colour,  as  chlorine,  which  is  green. 

The  atmosphere  which  surrounds  the  earth,  as  well  as  solids 
and  liquids  upon  its  surface,  is  retained  there  by  its  gravity  or 
weight.  This  will  be  made  evident  as  we  proceed. 

216.  It  is  the  resistance,  occasioned  by  the  inertia  of  air,  that 
causes  all  bodies  which  are  put  in  motion  in  it  gradually  to 
come  to  a  state  of  rest ;  at  the  same  time,  a  portion  of  its 
own  particles  is  put  in  motion  by  a  solid  or  liquid  projected 
in  it. 


Quest.  214.  By  what  is  the  earth  constantly  surrounded  ?  Why  is  not  the 

Eressure  of  the  atmosphere  perceptible  ?  Does  it  obey  the  same  laws  as 
quids  ?  Are  there  other  gases  besides  atmospheric  air  ?  Have  all  the  same 
mechanical  properties  ?  215.  Is  air  material  ?  Has  it  the  properties  of  matter, 
as  weight,  impenetrability,  inertia,  &c.  ?  Has  it  any  colour  ?  How  is  this 
shown  ?  How  is  the  air  retained  upon  the  earth  ?  216.  Why  do  bodies  put 
in  motion  in  the  air  soon  come  to  a  state  of  rest?  How  is  this  shown  by 
means  of  the  apparatus  represented  in  figure  99  ?  Why  do  both  mills  move 
equally  long  in  the  exhausted  receiver,  though  one  stops  much  before  the 
other  when  made  to  revolve  in  the  open  air  ?  By  what  means  do  birds  sus, 


PNEUMATICS. 


109 


Fig.  99. 


This  property  is  well  illustrated 
by  the  following  apparatus.  A  and 
B,  figure  99,  are  two  separate 
movable  axes,  each  having  four 
fans  or  vanes  composed  of  thin 
slips  of  brass  inserted  in  it  by  one 
end.  In  one  of  them,  A,  they  are 
inserted  edgewise ;  that  is,  so  that 
when  the  axis  is  turned,  the  edges 
are  presented  in  the  direction  of 
the  motion  ;  but  in  B,  they  are  in- 
serted so  that  the  faces  are  pre- 
sented in  the  direction  of  the  mo- 
tion. C  and  D  are  two  springs  of 
equal  strength  which  are  made  to  act  against  pins  in  the  axes 
A  and  B,  and  turn  them,  a  slider  not  represented  in  the  figure 
holding  them  in  place  until  everything  is  in  readiness.  By 
means  of  the  slider,  both  are  set  in  motion  at  the  same  time, 
and  with  equal  velocities;  but  as  the  resistance  of  the  air  to  B 
is  much  greater  than  to  A,  in  consequence  of  the  different  po- 
sitions of  the  vanes,  it  comes  to  rest  much  sooner  than  the 
other.  If,  however,  they  are  placed  under  the  receiver  of  an 
air-pump,  and  the  air  exhausted,  they  will  be  found  upon  being 
again  put  in  motion  as  before,  to  move  with  equal  velocities, 
and  to  continue  in  motion  the  same  length  of  time.  It  is  this 
property  which  enables  birds  ($  60)  to  raise  themselves  in  it, 
by  means  of  their  wings,  above  the  surface  of  the  earth.  The 
wings  being  spread  and  struck  on  the  broad  surface  of  the  air 
beneath  them,  are  resisted,  by  the  inertia  of  the  air,  which 
forms  a  fulcrum  or  prop,  on  which  the  bird  rises  by  the  "lever- 
age of  its  wings." 

217.  As  the  lower  parts  of  the  atmosphere  must  constantly 
sustain  the  weight  of  the  upper  portion,  they  are  pressed  toge- 
ther with  great  force,  and  their  density  much  increased.  As 
we  ascend  above  the  surface,  the  density  of  the  air  rapidly 
diminishes,  and  at  the  height  of  about  3  miles  is  reduced  to 
one-half;  at  the  height  of  6  miles,  to  one-quarter ;  and  at  the 
height  of  9  miles,  to  only  one-eighth  of  its  density  at  the  level 
of  the  sea  It  extends  to  the  height  of  about  40  or  45  miles  ; 
but  if  it  had  a  uniform  density  equal  to  its  present  density  at 
the  surface,  its  height  would  be  only  about  5  miles.  The  whole 
mass  of  the  atmosphere  surrounding  the  earth  is  computed  to 
be  equal  to  that  of  a  sphere  of  lead  a  little  more  than  60  miles 
in  diameter ;  upon  the  supposition  that  the  earth  is  a  perfect 

tain  themselves  in  the  air  ?  What  serves  as  the  prop  for  their  wings  ?  217. 
Why  are  the  lower  parts  of  the  air  more  dense  than  the  more  elevated  por- 
tions ?  What  is  the  density  of  the  air  at  the  height  of  3  miles  ?  What  at  the 
height  of  9  miles  ?  How  high  does  the  atmosphere  extend  ?  If  the  whole 
atmosphere  was  reduced  to  a  uniform  density  equal  to  that  at  the  surface, 


110  NATURAL     PHILOSOPHY. 

sphere,  8000  miles  in  diameter,  and  that  the  height  of  the  atmo- 
sphere, if  it  was  of  uniform  density,  would  be,  as  above  stated, 
5  miles.  The  specific  gravity  of  lead  and  air  are  taken  as  they 
are  set  down  in  recent  approved  tables.  The  student  who  has 
some  knowledge  of  mathematics  will  find  the  calculation  a 
pleasing  and  not  a  tedious  operation. 

218.  We  have  seen  above  (§  14)  that  though  the  attraction 
of  cohesion  among  the  particles  of  liquids  is  small,  yet  it  is  not 
altogether  wanting;  but  the  particles  of  aeriform  fluids,  so  far 
from  showing  any  attraction  for,  actually  repel  each  other,  and 
are  kept  together  or  in  the  close  vicinity  of  each  other,  only 
by  external  pressure.     A  mass  of  air,  therefore,  always  ex- 
pands as  soon  as  any  portion  of  the  pressure  to  which  it  is 
subjected  is  removed. 

219.  Wind  is  nothing  more  than  the  air  in  more  or  less  rapid 
motion,  and,  like  other  bodies,  its  force  depends  upon  the 
quantity  put  in  motion  and  its  speed.  (§  95).     The  effects  of 
this  force  are  seen  in  the  motion  of  ships  which  are  propelled 
by  it  through  the  sea,  in  the  motion  of  the  windmill,  and  in  the 
terrible  devastations  of  the  hurricane,  as  it  sweeps  before  it 
trees,  and  buildings,  and  everything  movable  with  which  it 
comes  in  contact. 

The  weight  of  the  air  present  in  any  given  space,  as  an  apartment  in  a 
building,  is  much  greater  than  most  persons  generally  suppose.  Suppose 
a  gentleman's  parlour  to  be  20  feet  square  and  12  feet  high,  taking  the 
weight  of  100  cubic  inches  of  air  at  31  grains,  (the  true  weight  is  31.01 
grains,)  the  weight  of  the  whole  air  in  the  room  will  be  found  on  calcula- 
tion to  be  more  than  367  pounds  avoirdupoise.  Let  the  student  make  the 
estimate. 

AIR-PUMP. 

220.  The  air-pump  is  indispensable  in  demonstrating  the 
various  properties  of  the  air  and  other  gases ;  and  we  therefore 
give  a  description  of  it  before  proceeding  further. 

This  instrument,  in  its  most  simple  form,  consists  of  a  barrel, 
A  B,  figure  100,  usually  made  of  brass,  and  carefully  turned  out 
inside,  so  as  to  admit  of  the  piston,  P,  which  is  very  accurately 
fitted  to  it,  to  move  freely  up  and  down  in  it  by  means  of  the 
handle,  H.  At  the  bottom,  a,  is  a  small  valve  opening  upward, 
made  very  light,  which,  when  shut,  perfectly  closes  the  small 
aperture  beneath  it.  It  is  represented  in  the  figure  as  open. 
In  the  piston,  P,  is  another  similar  valve,  b,  which  also  opens 

what  would  be  its  height  ?  What  would  be  the  diameter  of  a  solid  globe  of 
lead  to  contain  the  same  amount  of  matter  as  is  contained  in  the  atmosphere  ? 
218.  Is  there  any  cohesion  among  the  particles  of  air  ?  What  only  keeps 
the  particles  in  the  vicinity  of  each  other  ?  What  is  always  the  effect  of 
removing  the  pressure  upon  a  volume  of  air  ?  219.  What  is  wind  ?  In  what 
do  we  see  its  effects  ?  What  is  the  quantity  of  air  ordinarily  present  in  a 
room  20  feet  square  and  12  feet  high  ?  220.  How  is  the  air-pump  construct- 
ed in  figure  100  ?  How  is  its  action  explained  by  figure  100  ? 


PNEUMATICS. 


Ill 


Fig.  100. 


upward.  Now,  when  the  piston  is  pressed  down- 
ward, the  valve  in  it  is  opened  by  the  air  in  the 
barrel  beneath  it,  which  is  prevented  from  escap- 
ing by  the  valve,  a ;  but  it  closes  by  its  own 
weight  as  soon  as  the  piston  reaches  the  bottom. 
When  the  piston  is  raised,  the  valve,  6,  in  it  be- 
ing closed,  all  the  air  in  the  barrel  above  it  is 
lifted  out,  and  a  vacuum  would  be  produced 
below  it  but  for  the  air  rushing  in  through  the 
valve,  a,  at  the  bottom. 

221.  Suppose  the  barrel  to  be  now  screwed  on 
to  a  globular  vessel,  C,  fitted  with  a  stop-cock, 
which  we  will  suppose  open.  As  the  piston, 
P,  is  raised,  the  air  from  without  not  being  per- 
mitted to  enter  the  space  in  the  barrel  below,  it 
can  be  filled  only  by  the  expansion  of  the  air  in 
the  vessel,  C,  which,  in  consequence  of  its  elas- 
ticity, (a  property  to  be  illustrated  more  fully 
hereafter),  will  immediately  take  place.  When 
the  piston  again  descends,  the  lower  valve,  a, 
closes,  and  the  air  in  the  barrel  is  condensed, 
until  it  becomes  equal  in  density  to  the  surround- 
ing atmosphere;  the  further  descent  of  the  piston 
will  then  cause  the  upper  valve,  6,  contained  in 
it,  to  open  and  allow  the  air  below  it  to  escape. 
As  the  piston  again  ascends,  a  further  expansion 
of  the  air  in  the  vessel,  C,  takes  place  to  fill  the 
barrel  by  the  opening  of  the  lower  valve ;  and 
thus,  by  the  working  of  the  piston,  successive 


portions  of  the  air  in  C  are  removed,  until  at  length  its  elasti- 
city becomes  so  feeble,  by  reason  of  the  small  quantity  which 
remains  within,  that  it  is  incapable  of  lifting  the  valve  a,  when 
of  course  the  further  exhaustion  must  cease.  It  will  be  seen, 
therefore,  that  the  air-pump  is  incapable  of  producing  a  perfect 
vacuum.  By  turning  the  stop-cock,  the  vessel,  with  the  small 
quantity  of  air  it  contains,  may  be  separated  from  the  pump 
by  unscrewing  it  at  B. 

To  the  simple  air-pump  of  this  construction,  the  name 
syringe,  or  exhausting  syringe,  is  often  applied.  There  are 
various  modifications  of  it,  which  it  is  not  necessary  here  to 
describe. 

222.  Such  a  pump  would  be  effectual,  but  of  course  slow,  in 
its  operation.  In  order  to  make  the  instrument  exhaust  more 
rapidly,  and  to  adapt  it  better  for  use,  it  is  generally  made  with 


Quest.  221.  Does  the  air-pump  remove  all  the  air  from  a  vessel  ?  Why 
can  it  not  produce  a  perfect  vacuum  ?  Does  the  quantity  removed  by  each 
elevation  of  the  piston  constantly  diminish  ?  222.  Why  is  the  common  air- 
pump  made  with  two  barrels  ?  How  do  these  barrels  connect  with  the  plate 


112 


NATURAL     P  H  I  L  O  S  O  T  H  Y. 


Fig.  101. 


two  barrels,  and  provided  with  other  conveniences,  as  de- 
scribed below. 

Figure   101    represents   an   air- 
pump  of  the  ordinary  construction. 
A  A  are  the  two  barrels  provided 
with  valves  and  pistons  precisely 
like  that  represented  in  figure  100. 
At  the  bottom  they  connect  with  a 
small  tube,  I,  which  extends  in  to 
the  centre  of  the   large  circular 
plate,  C,  so  that  when  the  pump  is 
worked,  the  air  is  drawn  in  at  the 
aperture  in  the  centre.     The  sur- 
face of  this  plate  is  ground  perfectly 
plain  and  smooth,  so  as  to  make  an 
air-tight  joint  with  a  glass  receiver, 
R,  figure  102,  which  has  its  lower 
edge   ground   and   polished   in   a 
similar  manner.     I  and  C  are  supposed 
to  correspond  to  the   same  letters  in 
figure  101.     By  the  side  of  the  barrels, 
A  A,  figure  101,  are  two  pillars  screwed 
firmly  into  the  board  which  constitutes 
the  base  of  the  instrument,  and  designed 
to  support  a  concealed  toothed  wheel 
that,  by  means  of  the  handle,  works  the 

Eiston-rods,  seen  at  the  top  of  the  figure, 
i  front  of  the  barrels  is  a  small  stop- 
cock, not  shown  in  the  figure,  which  opens  into  the  tube,  I,  to 
let  in  the  air  when  necessary,  after  an  exhaustion  has  been 
produced.  When  any  substance  is  to  be  submitted  to  experi- 
ment, it  is  put  on  the  plate,  C,  the  receiver  placed  over  it  and 
the  air  exhausted. 

To  enable  the  operator  to  exhaust  the  air  from  vessels  of  other  forms, 
besides  that  of  the  receiver,  R,  described  above,  a  thread  is  usually  cut  in 
the  hole,  C,  in  the  centre  of  the  plate,  into  which  a  tube  may  be  screwed. 

The  air-pump  has  from  time  to  time  been  constructed  in  a  great  variety 
of  forms  besides  the  above,  which,  however,  fully  illustrates  the  principle 
on  which  it  acts. 

223.  The  condensing-  syringe  is  the  converse  of  the  exhaust- 
ing syringe,  or  air-pump  just  described,  and  is  designed  to 
condense  the  air  or  increase  its  density. 


ji'iimiiiiiiimii 


of  the  pump  on  which  the  receiver  is  placed?  What  is  the  usual  form  of  the 
receiver  used  with  an  air-pump  ?  How  are  the  pistons  worked  ?  Where  is 
the  substance  placed  that  is  to  be  submitted  to  experiment  ?  How  may  other 
vessels  be  connected  with  the  pump  so  as  to  have  the  air  exhausted  from 
them  ?  223.  What  is  the  design  of  the  condensing  syringe  ?  How  is  it  con- 
structed ?  In  what  direction  must  the  valve  open  ? 


PNEUMATICS.  113 


This  consists  of  a  brass  barrel,  furnished  with  a 
valve,  E,  figure  103,  opening  downwards,  and  hav- 
ing a  perforation  in  the  side  at  A.  The  piston,  B,  is 
"•  solid,  and  when  it  is  pressed  down  it  forces  the  air 
in  the  barrel  through  the  valve,  E.  On  raising  it,  the 
air  is  prevented  from  following  it  by  the  closing  of 
the  valve  E,  and  a  vacuum  is  formed  until  it  reaches 
the  aperture,  A,  when  a  fresh  portion  of  air  enters, 
to  be  in  turn  forced  through  the  valve  E.  By  means 
of  the  screw  at  the  bottom,  this,  like  the  exhausting 
syringe,  may  be  attached  to  a  vessel  as  the  globe  C, 
figure  100;  and,  by  working  it,  successive  portions 
of  air  could  be  driven  in  as  long  as  the  strength  of 
the  vessel  is  sufficient  to  retain  it. 

Fig.  103. 

By  means  of  these  two  pieces  of  apparatus,  all  the  important  experi- 
ments  illustrating  the  general  properties  of  gaseous  bodies  may  be  per- 
formed. 

PRESSURE    AND     ELASTICITY    OP    THE    AIR. 

224.  As  the  air  is  confined  to  the  earth  by  its  gravity  or 
weight  (§  215)  it  must  of  course  press  upon  the  earth's  surface 
precisely  as  any  other  substance  would.  This  pressure,  though 
the  ancient  philosophers  were  entirely  ignorant  of  its  existence, 
may  be  shown,  and  its  amount  accurately  ascertained  by  se- 
veral very  simple  experiments. 

225.  If  a  glass  of  the  form  of  B,  figure 
104,  having  a  piece  of  bladder,  A,  tied 
over  it  when  wet,  and  then  allowed  to 
dry,  is  placed  upon  the  plate  of  the  air- 
pump,  and  the  air  gradually  exhausted, 
the  piece  of  bladder  will  at  first  be  seen 
to  curve  down  ward  by  thepressure  above, 
and  at  length  it  will  give  way  with  a  loud 
report. 

If,  instead  of  the  piece  of  bladder,  A, 
the  palm  of  the  hand  be  placed  on  the 
Fig.  104.  glass,  upon  the  exhaustion   of  the   air 

from  beneath,  it  will  be  held  down  with 
such  a  force  as  to  make  it  difficult  to  remove  it  without  first 
readmitting  the  air. 

Quest.  224.  Does  the  air  press  upon  the  surface  of  the  earth  just  as  other 
bodies  ?  Were  the  ancient  philosophers  acquainted  with  this  property  of  the 
air  ?  225.  How  is  the  pressure  of  the  air  shown  by  a  piece  of  bladder  tied 

10* 


114  NATURAL     PHILOSOPHY. 

If  a  piece  of  thin  plate  glass  were  used,  it  would  be  incapable 
of  resisting  the  pressure,"and  would  be  broken. 

226.  In  these  experiments,  before  the  exhaustion  of  the  air 
from  the  glass  receiver,  the  downward  pressure  upon  the  piece 
of  bladder  or  upon  the  hand,  is  of  course  the  same  as  after- 
wards; but  it  is  counterbalanced  by  the  upward  pressure  of 
the  air  within ;  when  this  is  removed,  the  effects  of  the  down- 
ward pressure  are  seen  as  above  shown. 

If  a  glass  tube,  A  B,  figure  105,  closed  at  one 
end,  be  partly  filled  with  water,  and  the  finger 
held  upon  the  open  end  to  prevent  the  escape  of 
the  water  until  it  can  be  inverted  and  immersed 
in  a  vessel,  C,  of  the  same  liquid,  upon  the  removal 
of  the  finger  it  will  be  found  the  water  will  not 
fall  to  the  surface  of  the  liquid,  DE,  in  the  vessel, 
but  will  remain  suspended  in  the  tube,  as  at  m. 

227.  If  the  tube,  instead  of  being  partly  filled  in 
this  manner,  had  been  open  at  both  ends,  and 
connected  with  an  air-pump,  as  the  air  was  ex- 
hausted the  water  would  gradually  rise  in  it  un- 
til it  was  quite  filled,  provided  its  perpendicular 
Fig.  105.       height  should  not  be  greater  than  about  33  feet. 
If  the  air  were  again  admitted,  the  water  would  instantly  fall  to 
its  former  level. 

Now,  the  stan  ding  of  the  water  in  the  tube  in  the  first  of  these 
experiments  above  the  level  of  that  in  the  vessel,  and  its  gra- 
dual rise  in  the  tube  in  the  second  experiment,  are  occasioned 
by  the  pressure  of  the  atmosphere  on  the  surface  of  the  water 
without  the  tube.  In  the  last  experiment,  before  the  exhaustion 
is  commenced,  the  air  presses  on  the  surface  of  the  water 
equally  both  within  and  without  the  tube ;  but  as  soon  as  the 
exhaustion  of  the  air  in  the  tube  is  commenced,  the  greater 
pressure  on  the  surface  of  the  water  outside  forces  a  portion 
to  enter  the  tube  to  supply  the  place  of  the  air  that  has  been 
removed.  When  the  water  has  risen  to  the  height  of  about  33 
or  34  feet,  the  column  is  just  balanced  by  the  atmospheric 
pressure,  and  no  exhaustion  will  produce  any  further  ascent. 


over  the  mouth  of  a  receiver  prepared  for  the  purpose  ?  If  a  plate  of  glass 
were  used  instead  of  the  piece  of  bladder,  what  would  be  the  effect  ?  226. 
What  if  the  palm  of  the  hand  were  used  ?  Why  is  not  this  downward 
pressure  ordinarily  perceptible  I  If  a  glass  tube  closed  at  one  end  is  partly 
filled  with  water,  and  the  finger  held  upon  the  open  end  until  it  can  be  in- 
verted and  held  in  a  vessel  of  water,  why  does  not  the  water  fall  upon  the 
removal  of  the  finger  ?  227.  If  the  tube  was  open  at  both  ends,  and  connect- 
ed by  another  tube  with  the  air-pump,  what  would  be  the  effect  of  exhausting 
the  air  ?  What  is  the  cause  of  the  standing  of  the  water  in  the  tube  above 
its  level  in  the  basin,  and  its  rise  in  the  tube  when  the  air  is  exhausted  ?  How 
high  will  the  water  rise  in  an  exhausted  tube  ? 


PNEUMATICS.  115 

228.  If  a  liquid  lighter  than  water  is  used,  it  will  rise  higher 
than  water,  in  proportion  as  its  specific  gravity  is  less. 

So  also  the  height  to  which  liquids  heavier  than  water  can 
be  made  to  rise,  will  be  less  than  34  feet,  in  proportion  as  their 
specific  gravity  is  greater  than  that  of  water. 

229.  This  is  well  illustrated  in  the  case  of  mercury,  which  is 
about  13^  times  as  dense  as  water.  Thus,  34  feet,  or  408  inches, 
divided  6y  13|,  gives  30f  feet,  which  is  about  the  height  to 
which  mercury  will  usually  be  found  to  rise. 

230.  As  the  column  of  mercury  which  will  be  sustained  by 
the  atmosphere  is  only  about  30  inches  in  height,  it  will  be 
easy  to  make  the  experiment  to  test  our  conclusions. 

Having  procured  a  tube  of  glass,  as  A  B,  figure 
106,  not  less  than  33  inches  in  length,  and  closed  at 
one  end,  fill  it  quite  full  of  pure  and  clean  mercury, 
and  then  pressing  firmly  against  the  open  end  with 
the  finger  to  prevent  the  escape  of  the  mercury,  in- 
vert it  in  a  vessel  of  mercury,  C,  and  remove  the 
finger.  Supposing  the  tube  to  be  33  inches  in  length, 
and  one  inch  at  the  bottom  immersed  beneath  the 
mercury  in  the  vessel,  the  height  of  the  column  will 
at  first  be  32  inches ;  but,  on  the  removal  of  the 
finger,  it  will  be  seen  instantly  to  fall  to  D  D,  and 
stand  there  at  about  30  inches,  the  space  in  the  tube 
above  this  being  entirely  empty. 

This   vacant  space   above    the    surface  of  the 
mercury  is  called  the  Torricellian  vacuum,  from 
the  name  of  the  individual  who  first  performed  the 
experiment.    It  is  usually  considered  the  most  per- 
fect vacuum  that  can  be  formed  by  man,  at  least 
when  the  proper  precautions  are  taken  in  forming  it. 
Fig.  IDS.         That  it  is  really  the  pressure  of  the  atmosphere 
which  sustains  the  mercury  in  the  tube  in  this  case, 
is  made  plain  by  placing  the  vessel  of  mercury  with  the  tube, 
under  a  tall  receiver  on  the  plate  of  the  air-pump,  and  ex- 
hausting the  air ;  the  mercury  will  be  seen  to  fall  as  the  ex- 
haustion proceeds ;  and,  if  a  perfect  vacuum  could  be  produced, 
it  would  fall   in  the  tube  quite  to  a  level  with  that  in  the 
vessel. 

Quest.  228.  If  a  liquid  lighter  than  water  is  used,  what  will  be  the  result  ? 
If  heavier,  will  it  rise  as  high  ?  229.  How  high  will  mercury  rise  in  an  ex- 
hausted tube  ?  Why  does  it  not  rise  as  high  as  water  ?  How  much  heavier 
is  mercury  than  water  ?  230.  How  may  the  experiment  be  made  with  mer- 
cury ?  Supposing  the  tube  to  be  33  inches  in  length,  what  will  be  contained 
above  the  mercury  ?  What  is  the  Torricellian  vacuum  ?  Is  it  the  most  per- 
fect vacuum  that  can  be  produced  ?  What  will  be  the  effect  if  the  tube  and 
mercury  are  placed  under  a  receiver,  and  the  air  exhausted  ?  Is  it  certain 
that  it  is  the  atmospheric  pressure  that  sustains  the  mercury  in  the  tube  ? 


116  NATURAL     PHILOSOPHY. 

231.  The  Barometer.  —  An  instrument  prepared  as  just  de- 
scribed constitutes  the  ordinary  barometer,  which  is  designed 
to  show  the  pressure  of  the  atmosphere,  and  any  changes  that 
may  take  place  in  it.  The  tube  is  generally  made  about  32  or 
33  inches  long;  and  at  the  upper  surface  of  the  mercury  a  scale 
is  placed,  very  accurately  divided  into  inches  and  tenths  of  an 
inch,  and  provided  with  a  vernier,  so  that  variations  of  a  hun- 
dredth of  an  inch  may  be  measured.  Instead  of  an  open  vessel, 
C,  in  which  the  mercury  is  here  contained,  a  wooden  cup  is 

Generally  used,  having  the  tube  cemented  into  the  top,  and  the 
ottom  made  of  leather,  so  as  to  yield  readily  to  the  atmo- 
spheric pressure.  The  object  of  this  is  to  prevent  accident  by 
the  spilling  of  the  mercury,  which  would  be  likely  to  happen 
if  the  cistern  containing  it  was  open.  On  the  other  hand,  if  the 
cistern  were  made  tight,  and  of  an  inelastic  substance,  it  is 
plain  that  the  mercury  within  would  not  be  affected  by  varia- 
tions of  atmospheric  pressure. 


In  figure  107,  A  B,  is  the  tube  which  is  glued  firmly 
into  the  wooden  cistern,  C,  which  is  kept  open  at 
the  bottom  until  the  mercury  is  introduced,  when  a 
piece  of  leather,  D,  is  glued  on.  When  brought  to 
its  proper  position,  this  leather  yields  sufficiently  to 
allow  the  mercury  to  fall  and  rise  to  some  extent  in 
the  tube,  and  the  mercury  is  not  liable  to  be  spilled 
as  just  stated.  - 

By  means  of  this  instrument  it  has  been  deter- 
mined that  the  pressure  of  the  atmosphere,  even  at 
the  same  place,  is  not  uniform ;  for,  though  it  usually 
sustains  the  mercury  at  the  height  of  nearly  30 
inches,  at  the  level  of  the  sea,  yet  it  will  sometimes 
fall  as  low  as  28  inches,  or  rise  as  high  as  31 
inches.  In  some  cases  these  changes  are  very  sud- 
|c  den,  but  usually  they  take  place  gradually. 

Fig.  107. 

232.  No  less  than  twelve  or  fifteen  modifications  of  this  instrument, 
besides  the  above,  have  been  proposed  by  different  individuals  ;  but  one 
only  will  be  described  here.  This  is  the  wheel  barometer,  invented  by 

Quest.  231.  What  is  the  design  of  the  barometer?  How  does  it  show 
changes  in  the  atmospheric  pressure  ?  How  is  the  barometer  made  so  as  to 
be  influenced  by  atmospheric  pressure,  and  at  the  same  time  prevent  the 
escape  of  the  mercury  ?  Why  might  not  the  cistern  be  made  perfectly  air- 
tight of  an  inelastic  substance  ?  Is  the  pressure  of  the  air  always  uniform  at 
the  same  place  ?  What  is  the  usual  height  of  the  mercury  at  the  level  of  the 
sea  ?  How  much  may  it  vary  above  and  below  30  inches  ?  232.  How  may 
different  modifications  of  this  instrument  have  been  produced  ?  Is  it  believed 


PNEU  MATICS. 


117 


Fig.  108. 


Hooke.  It  is  frequently  used  as  an  ornament  for  par- 
lours, "  to  give  them  an  air  of  Philosophy ;"  but  its  in- 
dications are  not  very  accurate.  It  is  made  just  as  the 
barometer  described  above,  except  that  instead  of  the 
cistern  at  the  bottom,  the  tube  is  bent  upward,  as  seen 
in  figure  108.  The  atmospheric  pressure  acts  upon 
the  surface,  F,  of  the  mercury,  and  sustains  the  co- 
lumn, E  K,  which  is  above  the  level,  F  K.  The  co- 
lumns, FB  and  BK,  support  each  other.  If  the 
pressure  is  at  any  time  increased,  the  surface,  F,  will 
be  depressed,  and  the  surface,  E,  will  rise  towards  A, 
by  an  equal  amount;  consequently,  the  difference  of 
level  between  F  and  E,  or  the  mercurial  column  which 
is  supported  by  atmospheric  pressure,  will  be  increased 
by  twice  the  space  through  which  F  is  depressed. 
When  the  pressure  of  the  atmosphere  is  diminished, 
the  surface,  F,  will  rise,  and  E  will  fall.  On  the  sur- 
face F,  a  weight  is  placed,  to  which  a  cord  is  attached, 
passing  over  a  wheel,  P,  with  an  index  or  pointer,  H, 
and  having  another  weight,  W,  at  the  other  end.  Now, 
as  the  surface  F  rises  or  falls,  a  similar  motion  of  the 
weight  on  its  surface  is  produced,  and  the  pointer  is 
made  to  turn  on  its  axis ;  and,  by  having  a  circular 
plate,  G,  properly  graduated  and  attached  to  the  in- 
strument just  behind  the  pointer,  the  variations  of  the 
height  of  the  mercurial  column  are  beautifully  indi- 
cated. Usually,  around  this  graduated  circle,  the  words  "  Fair,"  "  Stormy," 
&c.,  are  engraved,  as  if  these  states  of  the  weather  might  be  expected 
always  whenever  the  mercury  stands  at  the  height  indicated  by  them ; 
which,  however,  is  by  no  means  the  fact.* 

But  long  observation  has  fully  proved  that  there  is  a  connec- 
tion between  changes  in  the  height  of  the  barometric  column, 
and  changes  in  the  weather.  Thus,  it  is  said  that,  in  general, 
the  rising  of  the  mercury  indicates  fair  weather,  and  its  falling 
the  reverse.  When  a  very  sudden  and  great  fall  occurs,  espe- 
cially at  sea,  a  storm,  with  high  wind,  is  to  be  expected.  But 
none  of  these  indications  are  to  be  considered  by  any  means 
certain.  Instances  are  however  given,  in  which  captains  of 
vessels,  by  heeding  the  indications  of  the  barometer,  and  mak- 
ing seasonable  preparations  for  the  approaching  storm,  have 
saved  themselves  from  its  effects,  which  otherwise  would  very 
probably  have  been  disastrous.  The  dreadful  storm  that  oc- 
curred on  lake  Erie  the  last  autumn  (1844),  we  are  informed 
by  Mr.  Haskins,  a  scientific  gentleman  of  Buffalo,  was  plainly 
indicated  at  that  place  several  hours  before  its  commencement 
there,  by  a  sudden  and  unusual  fall  of  the  mercury  in  the  baro- 
meter. About  the  time  the  mercury  was  thus  falling,  several 

there  can  be  traced  some  connection  between  changes  in  the  weather  and 
changes  in  the  barometer  ?  What  does  the  rising  of  the  barometer  indicate  ? 
What  is  indicated  by  a  fall  ?  What  is  said  of  the  storm  of  1844  upon  lake 


118  NATURAL     PHILOSOPHY. 

steamboats  left  the  harbour,  and  were  wrecked,  and  many 
lives  lost  in  their  encounter  with  the  gale;  a  disaster  which 
might  have  been  avoided  had  they  been  provided  with  good 
barometers,  and  their  officers  acquainted  with  their  use. 

It  would,  without  question,  be  difficult  to  explain  fully  why 
this  relation  between  changes  in  the  state  of  the  weather  and 
changes  in  the  height  of  the  barometer  should  exist ;  but  it  is 
very  easy  to  conceive  that  a  storm  in  any  place,  which  is  only 
a  violent  commotion  in  the  atmosphere  there,  should  have  the 
effect  to  increase  or  diminish  the  pressure  in  places  in  the 
vicinity.  And,  as  storms  move  over  the  surface  of  the  earth, 
the  place  which  at  one  hour  is  only  in  the  vicinity  of  a  storm, 
may  shortly  afterwards  be  the  theatre  of  its  most  violent 
effects. 

When  used  for  this  purpose,  the  barometer  is  sometimes 
called  a  weather-glass. 

233.  The  syphon-gauge,  used  to  determine  the  degree  of  ex- 
haustion produced  by  an  air-pump,  is  a  barometer  of  a  peculiar 
construction.  It  is  evident  that  if  the  common  barometer  could 
be  placed  under  the  receiver  of  the  air-pump,  the  exhaustion 
produced  at  any  time  would  be  correctly  indicated  by  it,  a  fall 
of  one-half,  one-third,  or  one-fourth  its  length  showing  that  a 
corresponding  proportion  of  the  air  had  been  removed;  but  its 
length  is  so  great,  30  or  31  inches,  as  to  preclude  its  use. 

The  syphon-gauge,  figure  109,  is  composed  of 
a  glass  tube,  ABCD,  cemented  firmly  into  a 
brass  sockei  with  a  faucet  at  D,  the  part,  B  A, 
being  filled  with  clean  mercury.  The  mercury 
is  kept  in  its  place  by  the  atmosphere,  and  there- 
fore,  when  D  is  screwed  in  the  pump  so  as  to 
bring  it  in  communication  with  the  tube,  I,  of  the 
air-pump,  fig.  101,  leading  to  the  receiver,  whenever 
the  exhaustion  is  carried  beyond  a  certain  point  it 
will  fall.  Let  us  suppose  that  the  part,  A  B,  is  74 
inches  in  length,  which  is  one-fourth  of  30,  when- 
ever three-fourths  of  the  air  has  been  exhausted, 
the  column  of  mercury,  being  no  longer  support- 
Fig.  109.  ed,  would  begin  to  fall,  the  lower  surface  at  B 
rising  at  the  same  time.  If  a  perfect  vacuum  could  be  produced, 
both  surfaces  of  the  mercury  would  stand  at  the  line  mm,. 

It  has  been  said  above  that  the  height  to  which  a  column  of 
water  may  be  raised  by  atmospheric  pressure  is  about  34  feet, 
or  the  column  of  mercury  about  30  inches,  though  subject  to 
considerable  variation.  But  these  heights  apply  only  to  places 

Erie  ?  233.  What  is  the  design  of  the  syphon-gauge  in  the  air-pump  ?  How 
is  it  constructed  ?  When  this  gauge  is  ?i  inches  in  height,  how  far  must  the 
exhaustion  be  carried  before  it  is  affected  ?  Can  a  column  of  water  be  raised 
34  feet  above  the  surface  on  a  high  mountain  ?  What  is  the  reason  ?  Will 


PNE  U  M  ATICS.  119 

situated  near  the  ordinary  level  of  the  sea.  As  we  ascend  above 
this,  and  of  course  above  a  portion  of  the  body  of  the  atmo- 
sphere, the  mercury  in  the  barometer  is  observed  to  fall.  If 
the  atmosphere  was  of  uniform  density  at  all  distances  above 
the  surface,  this  fall  of  the  mercury  would  necessarily  be  uni- 
form; that  is,  if  an  ascent  of  100  feet  above  the  level  of  the  sea 
produced  a  fall  of  y^th  of  an  inch,  then  on  ascending  200  feet 
it  would  fall  T%ths  of  an  inch,  and  so  on  for  any  other  height. 
But  this  is  by  no  means  the  case ;  it  is  found  by  experiment 
that  the  mercury  falls  much  more  rapidly  while  ascending  the 
first  hundred  feet,  than  it  does  in  passing  through  the  second ; 
and  more  the  second  hundred  feet  than  in  the  third,  and  so  on. 
This  is  in  consequence  of  the  density  of  the  air  diminishing  as 
we  ascend  from  the  surface  by  reason  of  the  diminished  pres- 
sure, (§  217).  The  stratum  of  air  at  the  surface  is  pressed  by 
the  whole  weight  of  the  superincumbent  atmosphere ;  but,  as 
we  ascend  above  this,  the  quantity  of  the  superincumbent  fluid 
being  less,  the  pressure  will  be  less,  and  also  the  density. 

234.  It  is  found  that  at  3  miles  above  the  level  of  the  sea  the 
mercury  stands  at  about  15  inches,  the  height  of  the  column 
being  diminished  about  one-half  in  this  distance ;  and  it  has 
been  calculated,  that  at  the  height  of  9  miles,  it  would  stand  at 
3;  inches;  and  at  15  miles,  only  1  inch.  (§  217). 

235.  It  will  be  seen  from  the  above,  that  this  instrument  may 
be  used  for  the  measurement  of  heights ;  this  is  indeed  one  of 
the  most  important  purposes  it  serves.  But  to  ensure  accuracy 
in  the  results,  several  very  important  precautions  are  to  be 
taken.  One  of  the  chief  causes  which  affect  its  results  is  varia- 
tion of  temperature  between  the  stations  at  the  base  and  top 
of  the  mountain,  the  height  of  which  is  to  be  measured ;  but 
rules  have  been  devised  for  making  the  necessary  corrections 
for  this  and  other  sources  of  error;  and  the  heights  of  moun- 
tains, especially  at  a  distance  from  the  sea,  can  probably  be 
determined  as  accurately  by  this  instrument  as  by  any  other 
means,  and  with  much  less  expense  and  trouble. 

236.  The  weight  of  the  whole  atmosphere  is  equal  to  that  of 
a  sea  of  mercury  about  29  or  '30  inches  in  depth,  or  to  a  sea  of 
water  about  33  or  34  feet  deep.    Now,  a  column  of  mercury  an 
inch  square  and  30  inches  high,  weighs  very  nearly  15  pounds 
avoirdupois;  and  this,  therefore,  must  be  the  pressure  of  the 
atmosphere  upon  every  square  inch  of  the  earth's  surface.  And 
as  it  is  the  nature  of  a  fluid  at  any  point  to  press  equally  in 

the  mercury  in  the  barometer  descend  equally  for  every  ascent  of  100  feet  ? 

234.  What  is  the  height  of  the  mercury  in  the  barometer  3  miles  above  the 
surface  of  the  earth  ?    What  would  be  its  height  15  miles  above  the  surface  ? 

235.  May  the  barometer  be  used  for  measuring  the  height  of  mountains  ? 
What  precautions  must  be  taken  to  insure  accuracy  ?    236.  What  would  be 
the  depth  of  a  sea  of  mercury,  or  of  water,  that  would  have  a  pressure  upon 
the  surface  of  the  earth  equal  to  that  of  the  present  atmosphere  ?     What  is 
the  pressure  of  the  atmosphere  upon  each  square  inch  ?  How  great  pressure 


120 


NATURAL     PHILOSOPHY. 


every  direction  (§  152),  the  lateral  and  upward  pressures  at  any 
point  will  be  the  same;  hence,  though  constantly  subjected  to 
this  enormous  pressure,  we  feel  no  inconvenience  from  it,  nor 
are  our  motions  impeded  by  it.  The  body  of  a  man,  the  sur- 
face of  which  is  about  2000  inches,  must  constantly  sustain  a 
pressure  of  about  30,000  pounds,  or  nearly  14  tons.  It  is  easy 
to  see,  therefore,  that  if  the  downward  pressure  was  not  coun- 
terbalanced by  an  equal  pressure  in  the  opposite  direction,  we 
should  be  crushed  to  the  earth  by  a  force  altogether  irresistible. 

237.  Other  instances  of  the  effects  of  Atmospheric  Pressure. — 
Various  operations  in  nature  and  art.  which  we  daily  witness, 
are  dependent  upon   the  pressure  of  the  atmosphere.     The 
Magdeburgh  hemispheres  afford  an  instance. 

Two  hollow  brass  hemispheres,  A  and  B, 
figure  110,  are  accurately  ground  so  as  to  fit 
each  other  at  the  edges,  and  form  an  air-tight 
hollow  sphere.  One  of  them  has  a  tube  with 
a  faucet,  E,  and  screw,  C,  by  which  it  may 
be  connected  with  the  air-pump,  and  to  which 
a  ring  for  a  handle,  like  that  on  the  hemi- 
sphere, A,  may  be  screwed  after  it  has  been 
exhausted  and  separated  from  the  pump.  To 
exhaust  the  air,  the  two  hemispheres  are  to 
be  placed  together  with  a  little  tallow  in  the 
joint,  if  necessary,  to  make  them  perfectly 
tight,  and  it  is  then  to  be  screwed  into  the 
hole  in  the  centre  of  the  plate  in  the  air-pump. 
When  exhausted,  they  will  be  held  together 
by  a  strong  force,  so  that  two  persons  taking 
hold  by  the  rings  or  handles  will  hardly  be  able  to  separate 
them.  The  part,  F,  is  merely  a  stand  for  holding  the  hemi- 
spheres when  not  in  use. 

238.  If  a  circular  piece  of  tolerably  thick 
leather,  2  or  3  inches  in  diameter,  be  moisten- 
ed, and  then  placed  closely  upon  a  smooth 
surface,  it  will  adhere  with  considerable  force; 
if  it  be  placed  upon  a  smooth  stone,  and  a 
string  attached  to  the  centre,  the  stone,  though 
weighing  several  pounds,  may  be  lifted  by  it. 
This  is  owing  to  the  exclusion  of  the  air  from 
between  the  stone  and  the  leather,  the  draw- 
ing of  the  leather  at  its  centre  from  the  stone 
tending  to  produce  a  vacuum.     The  force 
with  which  the  two  surfaces  will  be  held  to- 
gether will  be  equal  to  about  15  pounds  for 

every  square  inch  of  the  surfaces  in  contact.  Fig  in. 

does  the  body  of  a  man  constantly  sustain  ?  Why  is  he  not  pressed  by  it  to 
the  earth  ?  237.  How  are  the  Magdeburgh  hemispheres  constructed  ?  How 
are  they  used  ?  238.  How  may  a  circular  piece  of  leather  be  made  to  adhere 
to  a  smooth  stone  by  atmospheric  pressure  so  as  to  lift  it  ? 


Fig.  110. 


PNEU  M  ATICS. 


121 


The  experiment  is  represented  in  figure  111  ;  S,  the  stone,  and 
L,  the  piece  of  leather. 

239.  The  ability  of  some  insects,  as  the  house-fly,  to  walk  on 
ceilings  and  other  smooth  surfaces  presented  downward,  and 
even  on  smooth  panes  of  glass,  is  said  to  be  owing  to  the  pecu- 
liar formation  of  their  feet,  by  which  they  are  made  to  adhere 
to  the  surface  in  the  manner  of  the  piece  of  leather  in  the  above 
experiment.  The  feet  of  the  common  tree-toad  of  New  Eng- 
land (Hyla  versicolor),  it  is  believed,  also  act  in  part  on  the 
same  principle. 

240.  Let  B,  figure  112,  be  a  receiver,  in  the  top 
of  which  a  piece  of  wood  is  accurately  fitted  with 
an  excavation,  A,  in  it,  into  which  some  mercury 
may  be  poured.     On  exhausting  the  air  from  B, 
by  placing  it  upon  the  plate  of  the  air-pump,  the 
mercury  will  be  forced  through  the  pores  of  the 
wood  by  the  external  pressure,  producing  a  beau- 
tiful shower  of  the  metal. 

241.  The  upward  pressure  of  the  air  may  be 
shown  very  beautifully  in  the  following  manner. 
Take  a  glass  tumbler,  or  other  taller  vessel  if  de- 

Fig.  us.       sired,  and  fill  it  with  water  quite  full,  and  carefully 

place  a  piece  of  paper  over  the  surface, 

pressing  slightly  upon  it  with  the  hand. 

Then  suddenly  invert  the  vessel  and  re- 

move the  hand  ;  the  water  will  be  retained 

in  it,  its  whole  weight  being  sustained  by 

atmospheric  pressure.   Usually,  the  surface 

will  curve  upward  a  little,  as  shown  in 

figure  113.    The  paper  serves  to  prevent 

the  water  from   breaking  and   falling  in 

drops  or  fragments. 

242.  Ink-bottles  are  sometimes  constructed  on 
this  principle,  of  the  form  represented  in  figure 
114.  The  design  is  to  prevent  the  drying  of  the 
ink,  which  is  occasioned  by  too  large  a  surface 
being  presented  to  the  atmosphere.  The  only 
opening  the  bottle  has  is  at  A;  by  turning  this 
upward  the  ink  may  be  poured  in,  and  when  the 
bottle  is  nearly  filled,  and  turned  back  to  its  up- 
right  position,  it  is  prevented  from  escaping  by 

the  atmospheric  pressure.     The  pen  is  introduced  at  A,  which  must  be 

of  sufficient  depth  for  this  purpose;  and  when  the  quantity  of  fluid  in  this 

part  is  sufficiently  reduced,  a  bubble  of  air  enters,  and  a  portion  of  the  ink 

in  the  body  of  the  vessel  is  permitted  to  descend.     The  only  disadvantage 

which  attends  the  use  of  this  ink-bottle  is  occasioned  by  the  expansion  of 

Quest.  239.  How  do  insects  adhere  by  their  feet  to  perfectly  smooth  sur- 
faces ?  240.  How  may  mercury  be  forced  through  the  pores  of  wood  ? 
241.  How  may  the  upward  pressure  of  the  air  be  shown  by  means  of  a  turn- 
bier  filled  with  water  ?  242.  How  is  the  ink  kept  in  the  ink-bottle  repre- 


Fig.  113. 


-  1H- 


122  NATURAL     PHILOSOPHY. 

the  air  above  the  ink  by  a  rise  of  temperature,  which  will  sometimes 
cause  the  fluid  to  flow  out  at  the  mouth,  A. 

243.  Elasticity  and  Compressibility  of  the  Air.  —  We  have 
seen  (217)  that  in  consequence  of  the  pressure  of  the  upper 
parts  of  the  atmosphere,  the  air  near  the  surface  is  much  more 
dense  than  at  more  elevated  positions.  There  is  no  limit  known 
to  the  amount  of  compression  by  pressure  which  atmospheric 
air  admits  of,  though  some  of  the  gaseous  fluids,  as  carbonic 
acid  gas,  chlorine,  &c.,  are  condensed  so  as  to  take  the  liquid 
form,  when  the  pressure  reaches  a  certain  limit  depending 
upon  the  temperature. 

It  is  found  by  experiment  that  the  volume  or 
bulk  of  air,  under  different  pressures,  is  less  as 
the  pressure  is  greater.  This  may  be  shown  as 
follows.  Let  A  B  C  D,  figure  115,  be  a  glass  tube, 
closed  at  D,  and  bent  in  the  form  represented ; 
and  let  mercury  be  poured  in  at  the  open  end  by 
inclining  the  tube  a  little  until  it  fills  the  bend,  BC, 
and  divides  the  tube  into  two  parts.  If  now  more 
mercury  is  poured  into  the  tube,  its  weight  will 
press  against  the  air  at  C,  and  cause  the  surface 
to  rise  towards  D.  We  will  suppose  sufficient 
mercury  is  poured  in  to  cause  the  surface,  C,  to 
rise  to  n,  compressing  the  air  in  CD  into  one- 
half  the  space  it  at  first  occupied,  which  will  re- 
quire the  column  in  the  part  A  B  to  be  about  30 
inches  in  height  above  the  line  mn.  The  volume 
of  air  in  C  D  is  therefore  diminished  one-half,  by 
the  pressure  of  a  column  of  mercury  30  inches  in 
height,  which  we  have  heretofore  learned  is  just 
equivalent  to  the  ordinary  pressure  of  the  atmo- 
Fig.  us.  sphere.  But  before  the  mercury  was  poured  in, 
the  air  in  C  D  was  under  the  pressure  of  1  atmosphere,  and, 
by  adding  as  much  more,  or  increasing  the  pressure  to  2  atmo- 
spheres, the  volume,  as  already  stated,  is  reduced  to  one-half. 
If  the  pressure  were  increased  so  as  to  be  equal  to  3  atmo- 
spheres, the  volume  would  be  reduced  to  one-third  ;  if  increased 
to  4  atmospheres,  it  would  be  reduced  to  one-fourth;  and  so 
on  for  any  other  pressure.  This  could  easily  be  shown,  if  the 
part  of  the  tube  A  B  was  of  sufficient  length,  by  continuing  to 
pour  in  mercury,  and  observing  the  height  of  the  column  and 
the  space  occupied  by  the  air  in  D.  When  the  column  of  mer- 
cury was  60  inches  in  height,  only  one-third  of  the  space,  C  D, 

sented  in  figure  114  ?  To  what  inconvenience  is  it  subject  ?  243.  Is  there 
any  limit  to  the  compressibility  of  the  air  ?  How  are  some  of  the  gases 
affected  by  strong  compression  ?  In  what  ratio  does  the  volume  diminish 
as  the  pressure  is  increased  ?  How  is  this  illustrated  by  means  of  the  appa- 
ratus represented  in  figure  115?  How  much  is  the  volume  diminished  when 


PNEUMATICS. 


123 


Fig.  116. 


would  be  filled  with  air;  and  when  the  column  of  mercury  at- 
tained the  height  of  90  inches,  the  air  in  C  D  would  be  com- 
pressed into  one-fourth  the  space  it  at  first  occupied,  &c. 

We  have,  then,  this  law,  usually  called  the  law  of  Mariotte, 
that  the  volume  of  a  gas  will  always  be  in  the  inverse  ratio  of 
the  pressure  to  which  it  is  subjected. 

244.  As  a  necessary  consequence  of  the  above  principle,  it 
must  follow,  that  the  elastic  force  or  expansive  power  of  a  por- 
tion of  air  will  increase  in  proportion  as  the  space  it  occupies 
is  diminished ;  and  the  elastic  force  is  diminished  in  proportion 
as  the  space  through  which  it  is  allowed  to  expand  is  in- 
creased. 

^  This  may  be  better  understood  by  the 

A-JJ**-,  following  illustration.  Let  A  BCD,  figure 
1 16,  be  a  cylinder  in  which  the  solid  piston, 
A  B,  moves  air-tight,  and  without  resist- 
ance from  friction ;  and  let  the  distance 
from  this  piston  to  the  bottom  of  the  cylin- 
der be  just  12  inches.  Let  us  suppose  the 
weight  of  the  piston  to  be  just  20  ounces ; 
then  the  elasticity  of  the  air  within  is  just 
sufficient  to  sustain  this  weight.  Now, 
suppose  a  weight  of  20  ounces  is  placed 
upon  the  piston,  which  will  make  the  whole 
weight  40  ounces.  The  elasticity  of  the  contained  air  not  now 
being  sufficient  to  sustain  the  piston,  it  will  fall  a  certain  dis- 
tance, until  the  air  is  so  much  compressed,  and  its  elasticity 
increased,  that  it  is  again  supported  in  the  position  seen  in 
figure  117.  By  measuring  AC  now,  the 
distance  will  be  found  to  be  just  6  inches, 
the  doubling  of  the  pressure  having  reduced 
to  one-half  the  volume  of  the  contained  air, 
and  at  the  same  time  doubled  its  elasticity, 
as  appears  from  the  fact  that  it  now  sus-A. 
tains  twice  the  weight  it  did  before. 

If,  now,  a  weight  of  20  ounces  more  were 
added  to  the  piston,  the  air  within  would 
be  further  compressed,  the  piston  descend-  c 
ing  to  within  4  inches  of  the  bottom.     The  Pig.  117. 

compressing  force  would  then  be  three  times  as  much  as  at 
first;  the  contained  air  would  be  reduced  to  one-third  of  its 
original  bulk ;  and  its  elasticity  would  be  three  times  as  great 
as  at  the  commencement  of  the  experiment. 

the  pressure  is  doubled,  trebled,  or  quadrupled  ?  What  is  the  law  of  Mari- 
otte ?  244.  How  is  the  elasticity  of  a  portion  of  air  affected  by  compression  ? 
How  is  its  elasticity  affected  when  it  is  allowed  to  expand  ?  How  is  this 
illustrated  by  reference  to  figure  116  ?  How  much  is  the  air  in  the  cylinder 
compressed  by  doubling  the  weight  of  the  piston  ?  Can  any  force  press  the 
piston  quite  to  the  bottom  of  the  cylinder  ? 


124 


NATURAL     PHILOSOPHY. 


A  further  addition  of  20  ounces  weight  to  the  piston  would  cause  it  to 
descend  another  inch,  thus  reducing  the  air  to  one-fourth  of  its  original 
volume,  and  increasing-  fourfold  its  elasticity.  If  still  more  weights  were 
added  to  the  piston,  the  same  proportion  would  be  observed  between  the 
pressures^  the  corresponding  volumes  of  the  air,  and  its  elasticity  ;  but  no 
force  could  compel  the  piston  to  descend  quite  to  the  bottom  of  the  cylin- 
der. 

245.  The  ordinary  elasticity  of  the  air  is 
of  course  just  sufficient  to  resist  the  ordi- 
nary pressure  of  about  15  pounds  to  the 
square  inch ;  but  this  force  will  sometimes 
produce  unexpected  effects.  If  a  square 
bottle,  Br  figure  118,  be  firmly  sealed,  so 
as  to  be  air-tight,  and  then  placed  under 
the  receiver  of  the  air-pump,  when  the 
air  is  exhausted  from  the  receiver  so  as 
to  remove  the  pressure  from  the  outside 
of  the  bottle,  the  expansive  force  of  the 
air  within  will  often  be  found  sufficient  to 
burst  it  outward. 

Fig.  118. 

246.  Let  a  bottle,  B,  figure  119,  be  partly  filled 
with  mercury,  and  a  tube  open  at  both  ends  be  in- 
serted air-tight  through  the  cork ;  when  it  is  placed 
under  a  tall  receiver,  A,  and  the  air  exhausted,  the 
elasticity  of  the  small  portion  of  air  in  the  bottle 
above  the  mercury  will  cause  the  mercury  to  be 
raised  to  a  height  corresponding  to  the  degree  of 
exhaustion  produced.    If  all  the  air  could  be  ex- 
hausted, the  mercury  would  rise  in  the  tube  to  the 
height  of  30  inches. 

The  elasticity  of  the  air  may  also  be  shown  by  suspending 
an  India-rubber  bottle  or  bladder,  containing  a  little  air, 
with  its  mouth  carefully  tied,  in  the  receiver  of  the  air-pump, 
and  exhausting  the  air.  As  the  external  pressure  is  removed 
from  the  bottle,  the  air  within  it  expands,  causing  it  to  be 
greatly  enlarged.  When  the  air  is  again  admitted  into  the 
receiver,  the  bottle  contraetst  the  volume  of  the  air  within  it 
being  again  reduced  as  at  first.  If  the  bladder,  instead  of 
being  suspended  so  as  to  hang  freely  in  the  receiver,  is  placed 
in  a  cavity  and  loaded  with  weights,  they  will  be  lifted  by 
the  expansion  of  the  air  in  the  bladder  when  the  receiver  is  exhausted. 

247.  The  lungs  of  animals  are  alternately  inflated  and  con- 
tracted, in  the  process  of  respiration,  in  a  manner  somewhat 
similar  to  the  above.    This  important  organ  of  animals  is  com- 

Quest.  245.  If  a  square  bottle  is  corked  and  sealed  perfectly  tight  in  the 
open  air,  what  will  be  the  effect  of  placing  it  under  the  receiver  of  the  air- 
pump  and  exhausting  the  air  ?  246.  How  may  the  elasticity  of  a  portion  of 
confined  air  be  made  to  elevate  a  column  of  mercury  in  a  tube  ?  247.  How  are 
the  lungs  of  animals  alternately  inflated  and  then  contracted  ?  What  do  the 


Fig.  1J9. 


PN  EU  M  ATICS. 


125 


Fig.  J20. 


posed  of  soft  elastic  fleshy  substance,  situated  in  the  chest,  and 
filled  with  air-cells,  which  communicate  with  the  external  air 
by  means  of  the  wind-pipe  and  nostrils.  By  means  of  the  dia- 
phragm and  ribs,  the  cavity  of  the  chest  is  made  alternately  to 
expand  and  contract,  by  which  corresponding  motions  of  the 
lungs  are  produced. 

Figure  120  will  serve  to  illustrate 
the  process.  Let  M  be  a  glass  re- 
ceiver, having  a  bladder,  A,  partly 
filled  with  air,  suspended  in  it,  com- 
municating with  the  external  air  by 
means  of  a  small  tube  passing  air- 
tight through  a  cork  at  B;  and  hav- 
ing the  bottom  closed,  also  air-tight, 
by  a  leather  bag,  D.  Now,  by  draw- 
ing out  this  part,  D,  by  the  hand,  in 
consequence  of  the  increased  capa- 
city of  the  receiver,  the  air  is  drawn 
in  through  the  tube,  B,  into  the  blad- 
der, and  inflates  it ;  but,  by  pressing 
upward  on  the  part  D,  as  shown  in  the  figure,  N,  the  air  in  the 
-bladder  is  again  forced  out  through  the  same  tube,  B,  into  the 
open  air.  By  moving  the  bag,  D,  backward  and  forward  in 
this  manner,  it  is  evident  the  air  in  the  bladder,  A,  will  be  kept 
constantly  moving  in  and  out  through  the  tube,  B,  precisely  as 
in  the  process  of  respiration.  In  respiration,  the  diaphragm 
and  muscles  of  the  ribs  serve  the  purpose  of  the  leather  bag, 
D,  causing  an  alternate  inspiration  and  expiration  of  the  air 
through  the  windpipe  and  nostrils. 

248.  This  constant  inspiration  and  expiration  of  air  from  the  lungs  of 
warm-blooded  animals  is  absolutely  necessary  for  their  existence.  The  air 
in  the  lungs  is  constantly  undergoing  a  change  which  unfits  it  for  the  sup- 
port of  life,  and  it  therefore  requires  to  be  renewed  by  fresh  portions ;  an 
object  which  we  see  is  admirably  accomplished  in  the  process  of  respira- 
tion just  described.  But,  if  a  person  or  animal  is  confined  in  a  small  close 
room,  by  continually  breathing  the  same  air,  the  same  change  as  takes 
place  in  the  lungs  will  after  a  time  be  produced  in  the  whole  air  of  the 
apartment.  Hence  arises  the  necessity  of  having  the  air  in  our  apartments 
constantly  changed ;  or,  in  other  words,  to  have  them  well  ventilated.  In 
ordinary  dwelling-houses,  in  which  the  apartments  are  large  in  proportion 
to  the  number  of  occupants,  and  opportunity  is  frequently  given  for  the 
passage  of  the  air  in  and  out  by  the  opening  of  doors,  there  is  no  need  of 
any  special  provision  being  made  for  their  ventilation ;  but,  when  large 
assemblies  are  to  remain  for  some  time  in  comparatively  small  rooms,  or 

lungs  of  animals  consist  of?  How  do  they  communicate  with  the  external 
air  ?  How  is  the  cavity  of  the  chest  alternately  expanded  and  contracted  ? 
What  is  illustrated  by  figure  120  ?  248.  Is  this  constant  inspiration  and  ex- 
piration of  air  necessary  to  animals  ?  Why  is  it  necessary  that  the  air  of  our 
apartments  should  be  constantly  changed  ?  Why  is  it  not  necessary  to  pro- 
vide special  means  for  ventilating  ordinary  dwellings  ?  When  large  assem- 


126  NATURAL     PHILOSOPHY. 

when  from  any  cause  there  is  not  a  free  communication  between  the  air 
of  an  apartment  and  the  external  atmosphere,  injurious  consequences  will 
be  certain  to  result  unless  some  means  are  contrived  to  produce  a  circula- 
tion of  the  air.  Various  means  have  been  suggested  for  this  purpose,  but 
usually  it  will  be  sufficient  if  a  tube  is  provided  leading  from  the  upper 
part  of  the  room  through  which  the  deleterious  air  of  the  room  may  escape, 
and  another  leading  from  the  lower  part  to  admit  the  fresh  air  from  with- 
out. The  impure  air,  as  it  comes  from  the  lungs  at  a  temperature  a  little 
above  that  of  the  surrounding  air,  immediately  rises  and  passes  out  by  the 
escape-tube,  while  a  fresh  portion  enters  to  supply  its  place.  If  the  apart- 
ment is  heated  by  a  fire,  the  circulation  of  the  air  will  be  increased.  The 
size  of  the  tubes  should  of  course  be  proportioned  to  the  size  of  the  apart- 
ment to  be  ventilated. 

249.  There  are  some  phenomena  attending  the  passage  of  air  through 
tubes,  and  its  escape  from  them  in  certain  circumstances,  which  are  not  a 
little  curious.  If  a  tube  be  made  of  tissue-paper,  6  or  8  inches  long,  and 
about  an  inch  or  a  little  less  in  diameter,  having  a  piece  of  wood  in  one 
end  with  a  hole  in  its  centre  a  quarter  of  an  inch  in  diameter,  on  blowing 
through  this  hole,  either  directly  or  by  means  of  a  small  tube,  the  paper 
•will  collapse,  plainly  indicating  the  production  of  a  partial  vacuum  within 
it.  This  we  may  suppose  to  be  occasioned  by  the  sudden  expansion  of  the 
air  on  escaping  from  the  small  tube  by  which  it  was  introduced  within  the 
paper  tube.  A  portion  of  the  air  within  the  paper  is  blown  away,  and  the 
tendency  of  the  air  outside  to  rush  in  and  supply  the  vacuum,  produces 
the  collapse  we  have  noticed. 

It  appears  that  the  escape  of  a  gas  from  a  tube  into  the  open  air  is 
always  attended  by  a  degree  of  rarefaction  about  the  mouth  of  the  tube, 
and  a  consequent  pressure  of  the  surrounding  air  towards  this  point  at 
certain  distances  around.  Let  a  person  cut  out  two  circular  pieces  of  thick 
paper  or  pasteboard  about  2£  or  3  inches  in  diameter,  and,  making  a  hole 
in  the  centre  of  one,  insert  in  it  the  end  of  a  small  tube,  as  a  quill ;  then, 
making  the  other  disc  of  paper  a  little  concave,  let  him  place  it  with  its 
concave  side  down  upon  the  first,  holding  them  in  a  horizontal  position, 
with  the  quill  downward.  If  now  a  strong  current  of  air  is  passed  through 
the  quill  by  the  mouth,  contrary  to  what  might  be  expected,  it  will  be 
found  quite  impossible  to  blow  off  the  upper  piece  of  paper.  The  air  blown 
through  the  quill  expands  and  escapes  at  the  edges  of  the  paper  discs,  a 
partial  vacuum  being  all  the  time  kept  up  between  them  sufficient  to  keep 
the  upper  one  in  its  place. 

If  the  discs  of  paper  are  applied  to  the  apparatus  represented  in  figure 
125,  the  same  phenomenon  it  is  said  will  be  witnessed  while  the  jet  of 
water  plays.  The  current  of  water  issuing  into  the  air  produces  to  some 
extent  the  same  effect  as  a  current  of  air. 

blies  are  to  remain  some  time  in  comparatively  small  rooms,  what  means 
should  be  provided  for  their  ventilation  ?  What  occasions  the  deleterious  air 
from  the  lungs  to  rise? 


PNEUMATICS, 


127 


MACHINES    FOR    RAISING    WATER  —  PUMPS. 


250.  Suction- Pump.  —  Pumps  for 
raising  water  are  variously  construct- 
ed, but  the  one  most  commonly  seen 
>is  the  suction-pump,  so  called  from 
the  peculiar  mode  of  its  action.  This 
instrument  is  essentially  the  same  as 
the  air-pump  already  described  (§  220) 
except  that  it  is  made  larger,  and  has 
much  larger  valves  to  permit  the  wa- 
ter to  pass  freely.  It  is  worked  by 
means  of  the  handle,  H,  figure  121, 
and  is  usually  a  little  enlarged  at  the 
top  to  form  a  reservoir  for  the  water, 
and  allow  it  to  escape  by  the  spout,  S. 
When  the  lower  part  is  immersed  in 
water,  and  the  handle  worked,  the 
first  effect  is  to  exhaust  the  air  from 
the  tube  beneath  the  piston,  P,  pre- 
cisely as  in  the  air-pump;  but  this 
causes  the  water  to  rise  gradually  to 
fill  the  vacuum  thus  produced,  until 
Fig.  121.  at  length  it  reaches  the  lower  valve, 

?/,  which  is  represented  in  the  figure 

as  open,  the  piston  being  supposed  to  be  rising,  and  the  valve 
v  in  it  of  course  shut.  After  it  has  become  filled  with  water,  at 
every  successive  elevation  of  the  piston,  the  water  issues  freely 
at  S. 

As  the  atmospheric  pressure  is  sufficient  only  to  raise  a  co- 
lumn of  water  to  the  height  of  about  33  or  34  feet,  it  will  be 
seen  at  once  that  in  this  pump  the  lower  valve  must  always  be 
placed  within  this  distance  of  the  surface  of  the  water ;  and  it 
is  therefore  unsuited  for  use  in  deep  wells,  or  in  any  case  where 
the  water  is  to  be  raised  to  a  greater  height  than  the  distance 
mentioned. 

Quest.  250.  Is  the  common  suction-pump  similar  to  the  air-pump  in  its 
construction  ?  Why  is  it  called  by  this  name  ?  When  the  lower  part  is 
placed  in  water,  what  is  the  effect  of  the  first  stroke  raising  the  piston  and 
upper  valve  ?  Why  does  the  water  rise  ?  On  depressing  the  piston,  why 
does  not  the  water  again  descend  ?  After  the  water  reaches  the  piston,  how 
is  it  made  to  pass  on  through  the  pump  ?  How  high  may  water  be  raised  by 
this  pump  ?  Why  may  it  not  be  raised  higher  ?  How  high  may  mercury  be 
pumped  ? 


128  NATURAL     PHILOSOPHY. 

251.  Forcing-Pump. — To  avoid  this  diffi- 
culty the  forcing-pump  is  sometimes  used, 
by  which  water  or  any  other  liquid  may  be 
raised  to  any  required  height.  Like  the 
pump  just  described,  it  is  formed  of  a  cylin- 
drical tube,  A,  figure  122,  to  which  a  smaller 
one,  B,  is  usually  attached,  leading  to  the 
water  of  the  well  or  cistern  from  which  it 
is  to  be  raised.  But  the  piston,  P,  is  made 
solid,  and  the  upper  valve,  v,  is  placed  in  a 
tube  or  spout  branching  off  from  the  main 
tube,  A.  At  v'  is  the  lower  valve  precisely 
as  in  the  suction-pump ;  and  the  water  is 
raised  to  this  valve  by  atmospheric  pressure 
just  as  in  that  pump.  Let  us  suppose  every- 
thing in  order,  and  the  lower  end  of  the 
pump  immersed  in  water;  by  the  first  ele- 
vation of  the  piston,  P,  a  vacuum  will  be 
formed  in  the  chamber  below  it,  and  the 
air  will  rush  in  through  the  lower  valve  i/, 
the  water  of  course  rising  to  supply  its  place.  When  the  piston 
is  again  depressed,  a  portion  of  the  air  below  it  and  above  the 
lower  valve,  r',  will  be  forced  out  through  the  upper  valve,  but 
will  be  prevented  from  entering  again  by  the  closing  of  the 
valve.  Upon  a  second  elevation  of  the  piston,  more  air  is 
again  drawn  up  through  the  valve  1?',  to  be  also  forced  up  by 
the  descent  of  the  piston  through  the  upper  valve,  v ;  and  this 
is  repeated  until  at  length  the  water  reaches  the  valves,  and  is 
made  to  pass  through  in  the  same  manner  as  the  air  has  done. 
At  every  elevation  of  the  piston  the  water  rises  through  the 
lower  valve,  and  every  time  it  is  depressed,  a  portion  is  driven 
onward  through  the  upper  valve  into  the  tube,  C,  by  which  the 
water  may  be  raised  to  any  required  height.  But  though  the 
height  to  which  water  may  be  raised  by  this  pump  is  unli- 
mited, yet,  as  it  is  raised  to  the  lower  valve  by  atmospheric 
pressure,  this  valve  should  never  be  placed  farther  than  the 
oft-mentioned  height  of  33  or  34  feet  above  the  surface  of  the 
water  in  the  reservoir. 

In  this  pump,  as  thus  constructed,  the  water  is  necessarily 
forced  out  of  the  pipe,  C,  in  successive  jets,  at  every  descent 
of  the  piston.  In  order  to  cause  it  to  flow  in  a  continued 
stream,  an  air-vessel  is  sometimes  added  to  the  lateral  pipe,  C, 
in  the  following  manner : 

Quest.  251.  How  is  the  forcing-pump  constructed?  Where  is  the  upper 
valve  placed  ?  How  is  the  water  raised  to  the  lower  valve  ?  Is  there  any 
limit  to  the  height  to  which  the  water  may  be  forced  by  this  pump  ?  In  a 
pump  constructed  in  this  manner,  how  will  the  water  be  forced  out  ?  Why 
is  this  necessary  ?  How  may  the  water  be  made  to  flow  in  a  continued 
stream  ?  How  does  the  air-vessel  operate  to  produce  this  effect  ? 


PNEUMATICS. 


129 


Fig.  123. 


D,  figure  123,  is  a  strong  vessel  made 
perfectly  air-tight,  except  the  valve  by 
which  it  connects  with  the  body  of  the 
pump,  and  the  tube  C,  which  extends 
nearly  to  its  bottom.  Now,  when  the 
water  is  forced  into  this  air-vessel  through 
the  valve  at  the  bottom,  the  air  contained 
in  it  is  driven  out  through  the  tube,  C, 
until  the  water  reaches  its  lower  extre- 
mity, E;  but,  as  the  surface  rises  above 
this  point,  all  that  remains  must  be  con- 
densed before  it  in  the  upper  part  of  the 
vessel.  In  proportion  as  this  air  is  thus 
condensed,  and  its  elasticity  increased, 
the  water  is  made  to  rise  in  the  tube,  C; 
and  will  at  length  pour  from  it  in  nearly 
an  equable  stream,  by  reason  of  the  uni- 
form pressure  of  the  condensed  air  in  the 
air-vessel. 


252.  The  Fire-Engine,  as  usually  made,  is  merely  a  large 
forcing-pump  of  this  construction,  adapted  to  throw  a  stream 
of  water  to  a  great  height  for  extinguishing  fires.  It  generally 
has  two  cylinders,  each  with  its  piston  and  valves,  so  situated 
by  the  side  of  the  air-vessel  that  the  water  from  both  is  forced 
into  it,  one  piston  ascending  and  the  other  descending  at  each 
stroke. 

A  flexible  leather  tube  called  a  hose, 
sometimes  of  one  or  two  hundred 
feet  in  length,  is  attached  to  the 
pipe,  C,  by  which  the  water  may  be 
carried  to  the  immediate  vicinity  of 
the  burning  building,  and  directed 
to  the  proper  points,  without  ex- 
posing the  machine  itself,  or  the  men 
who  work  it,  to  danger  or  inconve- 
nience from  the  heat.  Let  D  E, 
figure  124,  be  a  large  box  or  reser- 
voir to  contain  water ;  and  let  A  and 
B  be  two  cylinders  with  solid  pis- 
tons; and  C,  an  air- vessel,  with  a 
tube  leading  from  near  the  bottom 

through  its  top.  At  V  V'  V"  and  V"  are  valves,  the  first  and  last 
opening  upward,  and  each  of  the  others  opening  into  the  air- 
vessel.  If  we  now  suppose  the  pistons  to  be  worked  by  means 
of  the  handle  to  which  they  are  connected,  it  will  be  readily 

Quest.  252.  What  is  the  use  of  the  fire-engine  ?  What  does  it  generally 
consist  of?  What  is  the  use  of  the  hose  ?  Why  are  two  forcing-pumps  used  ? 
Is  the  water  driven  from  both  into  the  same  air-chamber  ?  Why  is  the  fire- 


130 


NATURAL     PHILOSOPHY. 


seen  that  from  both  cylinders  the  water  is  forced  into  the  air- 
vessel,  from  which  it  is  driven  by  the  elasticity  of  the  confined 
air,  in  the  manner  described  above. 

The  whole  apparatus  of  the  fire-engine  is  always  placed  on 
wheels,  so  as  to  be  readily  transferred  from  place  to  place, 
as  necessity  may  require.  There  is  generally  also  a  suction- 
hose  accompanying  the  machine,  which,  when  an  opportu- 
nity occurs,  as  is  often  the  case,  may  be  thrust  into  a  well  or 
cistern,  and  the  instrument  be  thus  made  to  supply  itself 
with  water  just  as  the  simple  forcing-pump  already  described. 
This  suction-hose  is  made  to  connect  directly  with  the  cylin- 
ders themselves,  by  means  not  indicated  in  the  figure;  so  that 
the  reservoir,  D  E,  is  not  then  brought  into  use. 

If  a  forcing-pump  is  not  at  hand,  nor  a 
model  of  the  fire-engine,  the  following 
piece  of  apparatus  answers  well  to  illus- 
trate the  principle  upon  which  the  air- 
vessel  acts  to  throw  the  jet  of  water.  Let 
A,  figure  125,  be  a  globular  vessel  partly 
filled  with  water,  having  a  tube,  B,  passing 
air-tight  through  the  neck  nearly  to  the 
bottom ;  after  removing  this  tube,  let  the 
condensing  syringe  ($223)  be  screwed  in 
its  place,  and  a  quantity  of  air  forced  in, 
which  is  done  by  unscrewing  the  cap,  D, 
in  which  it  is  fixed.  When  the  quantity 
of  air  forced  in  is  sufficient,  the  faucet,  C, 
is  to  be  turned,  the  syringe  removed,  and 
the  small  tube,  B,  replaced;  if  the  faucet, 
C,  is  now  opened,  the  water  gushes  out 
m  a  beautiful  jet  of  considerable  height, 
•  by  reason  of  the  elasticity  of  the  air  corn- 
Fig.  125.  pressed  within. 

If,  when  the  air  has  been  exhausted  from  a  receiver,  a  tube 
is  opened,  connecting  with  its  inside  and  a  vessel  of  water,  a 
beautiful  jet  will  play  into  the  receiver  merely  by  the  pressure 
of  the  atmosphere  on  the  surface  of  the  water  without. 

253.  The.  Lifting- Pump.  — The  lifting-pump  is  designed  to 
act  altogether  independently  of  atmospheric  pressure.  It  con- 
sists of  a  hollow  cylinder,  ABC  D,  figure  126,  the  lower  end 
of  which  is  immersed  in  the  reservoir  from  which  the  water  is 
to  be  raised.  At  the  proper  distance,  C  D,  from  the  bottom,  a 
valve  is  placed  opening  upward,  and  below  this  is  the  piston 

engine  placed  on  a  carriage  ?  Is  a  suction-hose  sometimes  connected  with  the 
engine  ?  How  may  a  jet  of  water  be  produced  by  means  of  a  strong  air-tight 
vessel  and  a  condensing  syringe  ?  253.  How  is  the  lifting-pump  designed 
to  act  ?  What  does  it  consist  of?  Where  is  the  piston  placed  ?  How  is  it 
worked  ?  Will  this  pump  raise  the  water  to  any  height  ? 


PNEUMATICS. 


131 


Fig.  126. 


with  a  valve  also  opening  upward;  the  pis- 
ton-rod, R,  passes  down  and  connects  with 
the  frame- work,  represented  in  the  figure,  by 
which  it  is  worked.  Above  C  D,  the  lube  is 
bent  so  as  not  to  interfere  with  it.  This 
pump  must  be  immersed  so  that  the  water 
may  reach  the  upper  valve;  then  when  the 
piston  is  forced  upward,  the  water  above 
it  is  made  to  open  that  valve  and  occupy  the 
pipe  above  C  D,  and  on  its  descent  is  kept 
there  by  the  closing  of  the  valve,  the  water 
at  the  same  time  entering  through  the  valve 
in  the  piston.  On  the  reascent  of  the  piston 
a  portion  of  water  is  again  forced  up  through 
the  upper  valve,  and  so  on  while  the  pump 
is  worked. 

254.  We  shall  describe  only  one  other  pump, 
called  the  double-acting  pump,  which  is  represented 
in  figure  127.  A  B  is  the  cylinder  in  which  the 
piston  plays  by  means  of  a  rod  passing  air- 
tight through  a  collar  at  A ;  and  C,  D,  E  and 
F  are  four  valves,  two  of  which  will  be  open 
and  two  shut  at  each  stroke  of  the  piston.  Let 
us  suppose  the  piston  to  ascend,  the  water 
above  it  will  be  raised,  causing  it  to  open  the 
valve,  D,  and  pass  on,  as  shown  by  the  arrow, 
through  the  pipe  leading  to  the  cistern  to 
which  the  water  is  to  be  conveyed  ;  and,  at 
the  same  time,  by  reason  of  the  vacuum  pro- 
duced below  the  piston,  it  will  rise  through 
the  valve,  F,  by  the  tube,  H,  leading  to  the  re- 
servoir below.  When  the  piston  is  made  to 
descend,  the  valves  D  and  F  will  be  instantly 
closed,  and  C  and  E  opened,  the  water  being 
forced  through  C  by  the  piston,  and  drawn 
through  E  by  atmospheric  pressure.  Pumps 
of  this  construction  are  used  at  the  Fairmount 
water-works  near  Philadelphia,  by  which  that 
city  is  supplied  with  water.  They  are  worked 
by  water-power. 

255.  In  the  philosophical  toy,  called  Hiero's  fountain,  a  jet  of 
water  is  produced  by  means  of  the  pressure  of  a  column  of 
water  acting  on  the  air  in  an  air-vessel.  It  is  formed  of  two 
vessels,  A  and  B,  figure  128,  which  we  will  suppose  made  of 
glass,  connected  together  by  the  tubes  C  and  D,  which  pass 
air-tight  through  brass  caps  cemented  upon  the  necks  of  the 
globular  glass  vessels.  The  tube,  C,  passes  from  the  upper  part 

Quest.  255.  How  is  the  piece  of  apparatus  called  Hiero's  fountain  form- 
ed ?  By  what  means  is  the  air  compressed  in  the  upper  vessel  so  as  to 
produce  the  jet  ? 


Fig.  127. 


132 


Fig.  123. 


NATURAL     PHILOSOPHY. 

of  the  vessel,  A,  to  the  upper  part  of  B;  while 
the  tube,  D,  connects  the  basin,  E,  with  the 
lower  part  of  the  vessel,  B.  To  use  the  appa- 
ratus, the  small  jet-pipe,  E,  is  first  removed, 
and  the  vessel,  A,  nearly  filled  with  water; 
then  the  jet-pipe  is  replaced,  and  more  water 
poured  into  the  basin  at  the  top,  which  passes 
at  once  by  the  tube,  D.  into  the  lower  vessel, 
B.  But,  as  soon  as  the  water  rises  in  the  vessel, 
B,  above  the  lower  end  of  the  tube,  D,  there 
being  no  passage  for  the  air  to  escape,  it  will 
be  condensed  by  the  rise  of  the  water  in  B, 
into  the  upper  part  of  both  vessels,  the  tube,  C, 
forming  a  communication  between  them.  By 
opening  now  the  faucet,  E,  seen  above  the  wa- 
ter in  the  basin,  a  beautiful  jet  d'eau  is  produced 
by  the  water  issuing  from  the  upper  vessel 
through  the  central  tube. 

256.  Bellows.— The  various  kinds  of  bellows 
in  use  are  properly  air-pumps  for  forcing  this 
element  in  some  particular  direction  or  place. 
The  common  hand-bellows  consists  of  two 
boards  which  are  connected  at  their  edges  by 
pieces  of  leather  carefully  nailed  all  around, 
except  a  small  space  where  the  upper  board  is 


attached  to  the  lower  by  a  hinge ;  and  from  the  same  point  a 
small  tube  proceeds  called  the  nozle.  In  the  lower  board  is  a 
hole  covered  by  a  piece  of  thick  leather,  which  constitutes  a 
valve.  Now,  when  the  upper  board  is  raised,  a  vacuum  is  pro- 
duced within,  and  the  air  rushes  in  through  the  valve  in  the 
lower  board ;  and  when  the  two  boards  are  again  pressed  to- 
gether, a  strong  current  is  forced  out  through  the  nozle,  as 
every  one  has  seen. 

257.  In  the  case  of  the  bellows  described  above,  the  current 
of  air  from  the  nozle  is  of  course  suspended  every  time  the 
boards  are  drawn  apart ;  but  a  continuous  blast  may  be  pro- 
duced by  introducing  a  third  board  with  a  valve  between  the 
two  boards  of  the  above  bellows,  the  leather  being  nailed  to 
the  edges  of  the  three  boards.  This  constitutes  the  double  or 
forge-bellows.  It  is  in  fact  a  double  instrument.  When  the 
lower  board  is  raised,  the  air  within  the  lower  bellows  is  forced 
into  the  upper  through  the  valve  in  the  middle  board,  and  from 
this  it  is  forced  out  in  a  continuous  current  by  weights  placed 
on  the  upper  board.  This  bellows  may  be  seen  in  constant  use 

Quest.  256.  What  are  the  different  kinds  of  bellows  ?  How  is  the  common 
hand-bellows  constructed  ?  How  does  the  air  enter  when  the  instrument 
is  opened  ?  What  is  the  effect  produced  when  the  boards  are  pressed  to- 
gether ?  257.  In  these  bellows,  is  a  continuous  current  of  air  produced  ? 
How  may  the  bellows  be  constructed  so  as  to  produce  a  continuous  current  ? 


PNEUMATICS, 


133 


in  every  blacksmith's  shop;  occasionally,  though  rarely,  the 
form  is  modified;  but  the  principle  of  action  is  always  the 
same. 

258.  Within  a  few 
years  past,  the  sim- 
ple fan  used  in  the 
common  winnowing 
machine,  so  well 
known  among  far- 
mers, has  to  a  con- 
siderable extent  su- 
perseded the  bel- 
lows. ABD,  figure 
generally  used.  It 


Fig.  123. 


129,  is  a  side-view  of  the  instrument  as 
consists  of  a  cylindrical  box,  usually  not  more  than  3  or  4  feet  in 
diameter,  and  from  1  to  2  feet  in  the  other  dimension.  At  C, 
is  a  circular  aperture,  from  8  to  12  inches  in  diameter,  showing 
within  the  box  a  portion  of  the  four  fans  and  an  end-view  of 
the  axis  to  which  they  are  attached.  E,  is  a  side-view  of  the 
fans  attached  to  the  axis  removed  from  the  box.  Now,  suppose 
the  fans  in  their  place  in  the  cylindric  box  are  made  to  revolve 
rapidly  in  the  direction  indicated  by  the  arrow  at  E,  a  strong 
current  of  air  will  be  made  to  pass  out  through  the  aperture  or 
tube,  A  D,  a  corresponding  current  at  the  same  time  passing 
in  at  C. 

This  instrument  is  now  extensively  used  on  board  of  steam- 
boats that  use  anthracite  coal  for  blowing  their  fires,  and  also 
in  iron  and  other  furnaces.  In  the  common  winnowing  mill, 
as  already  remarked,  it  has  long  been  employed. 

259.  The  Syphon.  —  This  familiar 
hydraulic  instrument,  in  its  simplest 
form,  consists  of  a  bent  tube,  ABC, 
figure  130,  having  one  of  its  branches 
longer  than  the  other.  If  this  tube  be 
filled  with  water,  and  then  closed  by 
the  finger  to  prevent  its  escape  until 
the  shorter  branch  can  be  immersed 
in  a  vessel  of  water,  and  held  as  re- 
presented in  the  figure,  the  liquid  will 
immediately  commence  running,  and 
will  continue  to  flow  until  the  vessel 
is  exhausted.  It  will  serve  the  same  purpose  if  the  bent  tube 
is  first  immersed  in  the  water,  and  the  air  then  exhausted  from 
it  by  applying  the  mouth  at  C. 

Quest.  258.  What  instrument  is  now  used  to  a  considerable  extent  as  a 
substitute  for  the  bellows  ?  What  does  it  consist  of?  How  is  the  current 
of  air  produced  ?  What  use  is  made  of  it  on  board  of  steamboats  that  burn 
anthracite  coal  ?  258.  Of  what  does  the  syphon  consist  ?  How  is  the  tube 
to  be  filled  at  first  ? 
12 


Fig.  130. 


134 


NATURAL     PHILOSOPHY. 


260.  To  cause  the  flow  of  the  water  in  the  syphon,  it  is 
essential  that  one  branch  of  the  tube  should  be  longer  than  the 
other;  and  the  motion  is  always  towards  the  longer  branch. 
The  water  flows  out  of  the  longer  branch  in  consequence  of 
its  weight;  but  as  a  vacuum  would  thus  be  produced  in  the 
upper  part  of  the  tube,  the  water  from  the  vessel  rises  in  it  by 
atmospheric  pressure,  as  in  the  suction-pump.  If  the  longer 
leg  were  immersed  in  the  water  instead  of  the  shorter  one,  and 
then  filled  by  exhausting  the  air  by  the  mouth,  the  liquid  would 
immediately  flow  back  into  the  vessel.  The  length  of  the  branch 
immersed  in  the  vessel  is  always  to  be  measured  from  the  sur- 
face of  the  water,  D  E.  That  the  atmospheric  pressure  is  con- 
cerned in  the  operation  of  the  syphon  is  shown  from  the  fact 
that  it  entirely  fails  to  act  in  a  vacuum  ;  and  also  from  the  fur- 
ther fact  that  in  the  open  air  water  refuses  to  pass  a  syphon- 
tube,  the  shorter  leg  of  which  exceeds  34  feet. 

Large  syphon-tubes  have  been  used  for  practical  purposes, 
for  raising  water  many  feet  over  obstacles  that  it  would  be 
difficult  to  remove;  but  the  air  which  is  always  carried  in  with 
the  water,  being  set  free  by  the  diminished  pressure,  rises  to 
the  highest  part  of  the  tube,  and  after  a  few  hours  accumulates 
so  as  to  prevent  the  passage  of  the  water.  They  are  hence 
little  used  in  practice. 

261.  The  manner  in  which  the  syphon  acts 
is  well  illustrated  when  it  is  constructed  with 
an  air-vessel,  as  shown  in  figure  131,  which 
is  a  section  of  the  syphon-fountain.  B  is  an 
air-vessel,  supported  by  a  pillar  of  wood,  E, 
and  having  two  tubes,  A  and  C,  connected 
with  it,  of  which  the  first,  A,  may  be  consi- 
dered the  shorter  branch  of  the  syphon,  and 
C,  the  longer.  A  is  a  vessel  of  water  sup- 
ported by  a  shelf;  and  D,  a  second  vessel  to 
receive  it  after  being  discharged  from  the  in- 
strument. To  use  the  instrument,  the  air- 
vessel,  B,  with  the  tubes  attached,  is  to  be 
removed  from  its  support,  inverted,  and  the 
plug,  in  which  the  tubes  are  inserted,  un- 
screwed. The  air-vessel  is  then  to  be  filled 
about  a  third  full  of  water,  the  plug  with  the 
tubes  screwed  into  its  place,  and  the  whole 
restored  to  the  proper  position  upon  the 
Fig.  isi.  stand,  E ;  immediately  the  water  will  begin 

to  escape  from  B,  by  the  tube,  C,  producing 

Quest.  260.  Must  one  branch  of  the  tube  always  be  longer  than  the  other  ? 
In  what  direction  does  the  water  flow  ?  How  is  it  shown  that  the  pressure 
of  the  atmosphere  is  necessary  to  cause  the  water  to  flow  through  the  syphon  ? 
Why  may  not  large  syphons  be  used  with  advantage  for  practical  purposes  ? 
261.  How  is  the  syphon-fountain  constructed  ?  Is  a  partial  vacuum  produced 
in  the  air-vessel  ? 


PNEUMATICS.  135 

a  vacuum  within  it,  into  which  the  fluid  rises  from  the  vessel, 
A,  by  atmospheric  pressure.  If  the  tube,  C,  is  made  considera- 
bly longer  than  A,  with  a  bore  also  some  larger,  the  jet  of 
water  on  entering  the  air-vessel  may  easily  be  made  to  rise  to 
a  considerable  height. 

262.  It  is  to  be  observed  that  the  syphon  must  always  be 
first  filled  with  water  before  the  current  will  flow,  which  may 
be  done  either  by  filling  it  with  the  two  ends  held  upward  and 
then  suddenly  changing  it  to  its  proper  position,  or  by  first 
placing  it  in  this  position  and  then  exhausting  it  with  the 
mouth" or  by  means  of  an  air-pump.  The  same  effect  obviously 
will  be  produced  if  the  syphon  is  so  placed  with  reference  to 
the  reservoir  of  water,  that  the  fluid   may  rise  around  the 
shorter  branch  so  as  to  fill  it  quite  to  the  highest  point ;  the 
water  will  then  begin  to  be  discharged  through  the  longer 
branch,  and  will  afterwards  continue  to  flow,  even  though  the 
surface  of  the  water  in  the  reservoir  may  fall. 

The  philosophical  toy  called  Tantalus1 -cup  is 
constructed  on  this  principle.  It  consists  of  a 
cup,  figure  132,  with  a  syphon,  C  B  A,  in  it,  the 
short  leg  of  which,  C  B,  commences  near  the 
bottom  in  the  inside;  and  the  longer  leg,  BA, 
passes  down  through  the  bottom.  Now,  when 
water  is  poured  in,  it  will  rise  in  the  shorter  leg 
until  it  attains  the  highest  point,  B,  in  the  sy- 
phon, when  it  will  be  discharged  through  the 
longer  leg,  and  continue  to  flow  until  the  sur- 
face is  reduced  to  C.  A  small  image  of  a  man, 
supposed  to  represent  the  fabled  Tantalus,  (see 
Article  TANTALUS,  in  Anthorfs  Classical  Dic- 
tionary}, is  often  placed  over  the  syphon,  so  as  entirely  to  con- 
ceal it ;  and,  when  water  is  poured  into  the  vessel  gradually,  it 
rises  until  it  nearly  reaches  the  lips  of  the  image,  and  then  im- 
mediately subsides,  without  any  cause  being  visible  to  the  eye 
of  the  spectator.  Sometimes  the  syphon  is  concealed  in  the 
handle  of  the  vessel,  but  the  effect  is  the  same. 

263.  Intermittent  Springs.  —  The  phenomena  of  many  inter- 
mittent springs  may  be  explained  on  the  principle  of  the  syphon. 
Some  of  these  springs  ebb  and  flow  alternately,  and  others 
have  a  periodical  swell ;  a  much  greater  quantity  of  water  be- 
ing discharged  at  one  time  than  at  another,  the  changes  taking 
place  at  regular  intervals. 

Common  springs  are  evidently  merely  the  outlets  of  natural 
reservoirs  of  water  which  exist  in  every  part  of  the  earth,  and 

Quest.  262.  What  will  be  the  effect  if  the  water  is  made  to  rise  around  the 
shorter  leg  of  the  syphon  until  it  reaches  the  highest  part  of  the  tube  ?  How 
is  the  toy  called  Tantalus1  -cup  constructed  ?  What  is  the  effect  when  water  is 
poured  gradually  into  the  vessel  so  as  to  raise  the  surface  nearly  to  the  mouth 
of  the  image?  263.  What  are  intermittent  springs?  What  are  common 


136  NATURAL     PHILOSOPHY. 

are  filled  by  the  water  which  falls  upon  the  surface  in  rain  and 
snow,  and  gradually  percolates  through  the  soil.  When  these 
reservoirs  are  near  the  surface,  the  supply  of  water  sometimes 
ceases  during  long-continued  droughts,  and  the  springs  of 
course  become  dry ;  but  they  are  often  situated  so  deep  in  the 
hills  that  no  temporary  cause  of  this  kind  can  affect  them,  and 
they  continue  to  flow  at  all  times  alike. 

But,  if  the  aperture  or  channel  through  which  the  water  of 
the  reservoir  discharges  itself,  in  some  part  of  its  course  rises 
considerably  above  the  bottom  of  the  reservoir,  a  natural 
syphon  may  be  formed,  which  will  cause  the  spring  consti- 
tuting its  outlet  to  exhibit  an  intermittent  character. 

Let  AF,  figure  133,  be  a  sec- 
tion of  part  of  a  mountain  con- 
taining a  cavern,  C,  deeply- 
seated  in  it,  and  having  an  aper- 
ture or  channel,  D  E  F,  leading 
from  it  to  the  valley  or  plain  at 
its  base.  The  water  which 
falls  in  rain  and  snow  upon 
the  mountain  in  percolating 
through  the  soil,  will  find  its 
F'g- 133.  way  by  natural  fissures,  as  m  n, 

to  the  cavern  within,  and  gradually  fill  it,  until  the  surface  rises 
to  the  level  a  a  of  the  highest  point  E  in  the  aperture  leading 
from  it.  A  discharge  will  then  take  place  from  the  spring,  which, 
if  the  channel  is  sufficiently  large,  may  be  so  rapid  as  gradually 
to  reduce  the  quantity  of  water  in  the  cavern,  though  the  supply 
is  continued ;  but,  when  the  surface  has  fallen  to  the  level,  6  6, 
the  air  from  the  cavern,  C,  will  find  admission  into  the  passage, 
and  the  discharge  of  water  will  cease  until  the  reservoir  is 
again  filled  to  the  horizontal  level,  a  a,  as  before.  When  this 
takes  place,  the  passage  will  again  be  filled,  and  the  spring 
again  commence  flowing. 

If  the  part  of  the  channel,  E  F,  is  of  considerable  length, 
water  may  drain  directly  into  it  from  the  soil  in  sufficient  quan- 
tity to  cause  a  small  discharge  of  water  from  the  spring  while 
the  cavern  is  filling,  so  that  the  flow  may  never  entirely  cease. 
264.  The  Diving-- Bell.  — This  is  an  instrument  to  enable 
persons  to  descend  with  safety  beneath  the  surface  of  water. 
Though  persons  may  with  impunity  descend  unprotected  a 
considerable  depth  in  water,  it  is  well  known  they  can  remain 
but  a  short  time  before  they  are  obliged  to  come  again  to  the 

springs  ?  Why  do  these  springs  sometimes  fail  ?  Why  do  some  springs 
appear  to  discharge  very  nearly  the  same  quantity  of  water  uninfluenced  by 
the  weather  ?  How  may  a  natural  syphon  be  formed  in  the  passage  leading 
from  the  reservoir  ?  Why  in  such  a  case  would  the  water  cease  to  flow  at 
certain  regular  intervals  ?  What  may  prevent  the  water  from  entirely  ceasing 
to  flow  in  some  cases  ?  264.  What  is  the  design  of  the  diving-bell  ?  Can 


PNEUMATICS. 


137 


surface  to  receive  a  supply  of  fresh  air.  The  longest  period  a 
person  without  much  experience  may  remain  under  water 
with  safety,  is  said  to  be  only  about  half  a  minute ;  but,  by  long 
practice  and  painful  exertion,  one  may  at  length  become  so 
accustomed  to  the  effort  as  to  be  able  to  endure  the  depriva- 
tion of  air  it  requires  for  two  minutes.  A  few  instances  are  on 
record,  in  which  some  of  the  pearl-fishers  of  the  island  of  Cey- 
lon have  remained  beneath  the  water  four,  five,  or  even  six 
minutes ;  but  such  cases  are  exceedingly  rare.  But  even  this 
period  is  evidently  too  short  for  a  person  to  perform  any  im- 
portant operation  about  a  sunken  wreck,  or  in  preparing  to 
raise  large  articles  that  may  be  lying  upon  the  bottom. 

265.  By  the  assistance  of  the  diving-bell,  persons  are  enabled 
to  descend  to  great  depths,  and  remain  a  considerable  time. 
The  diving-bell,  in  its  simple  form,  is  merely  a  large  and  strong 
vessel  in  the  shape  of  an  ordinary  bell  or  receiver.  It  is  usually 
made  of  metal ;  and  if  constructed  of  wood,  it  must  be  loaded 
with  weights  to  cause  it  to  sink. 

When  a  descent  is  to  be  made,  the 
person  places  himself  inside,  as  re- 
presented in  figure  134,  on  a  seat 
prepared  for  the  purpose,  and  the 
attendants  let  the  apparatus  down  in 
the  water  by  means  of  a  rope.  As  it 
descends,  the  air  is  condensed  in  the 
upper  part  by  the  pressure  of  the  wa- 
ter ;  but  a  person  within,  it  is  found, 
experiences  little  if  any  inconve- 
nience. When  the  bell  nearly  reaches 
the  bottom,  a  signal  is  given  by  the 
person  within  to  the  attendants  above 
by  means  of  lines  passing  out  under 
the  edge,  and  the  whole  is  retained 
in  a  fixed  position,  while  exploration 
is  made  of  the  bottom  within  the  circle  of  vision  beneath.  When 
it  becomes  necessary,  the  apparatus  is  drawn  up,  and  its  posi- 
tion changed.  It  is  generally  let  down  from  on  board  a  ship. 

As  will  naturally  be  supposed,  a  person  cannot  remain  a  very  great 
length  of  time  below  the  surface,  even  in  a  diving-bell,  by  reason  of  the 
contamination  of  the  small  portion  of  air  within  by  his  breath.  The  vital 
principle  of  the  air  is  rapidly  absorbed  by  respiration;  and  if  no  new  sup- 

persons  unassisted  remain  for  any  considerable  time  under  water  ?  What  is 
the  longest  period  an  inexperienced  person  can  remain  under  water  with 
safety  ?  What  length  of  time  have  pearl-fishers  on  the  coast  of  Ceylon  in  a 
few  instances  remained  under  water  ?  265.  What  is  the  form  of  the  diving- 
bell  ?  What  is  it  usually  made  of?  Where  does  the  person  who  is  about 
to  descend  place  himself?  How  are  the  persons  within  enabled  to  give 
signals  to  their  attendants  above  the  water  ?  What  effect  is  produced  on  the 
12* 


Fig.  134. 


138 


NATURAL     PHILOSOPHY. 


ply  of  air  is  obtained,  the  person  will  in  time  as  surely  die  in  the  diving- 
bell  as  if  he  was  plunged  directly  into  the  water.  To  obviate  this  difficulty, 
an  air-pump  has  sometimes  been  used,  with  a  long  pipe  extending  from  it, 
by  which  fresh  air  from  the  surface  may  be  forced  down  under  the  bell. 
Various  contrivances  have  also  been  proposed  at  different  times  by  which 
persons  may  be  enabled  to  leave  the  chamber  of  the  bell  for  a  time  to 
search  the  bottom  in  its  vicinity. 

By  the  use  of  the  diving-bell,  and  apparatus  connected  with  it,  much 
valuable  property  that  had  been  sunk  in  the  sea  has  been  recovered,  which 
would  otherwise  have  been  totally  lost. 

It  has  recently  been  determined  that  a  person  diving-  from  a  bell, 
when  at  considerable  depth,  by  reason  of  the  condensed  state  of  the  air  in 
the  lungs,  can  remain  much  longer  immersed  in  the  water  than  when 
diving  directly  from  the  surface.  If  the  bell  is  supposed  to  be  at  the  depth 
of  34  feet,  the  volume  of  air  within  will  be  condensed  to  one-half  its  vo- 
lume at  the  surface  (§  243),  and  of  course  the  quantity  in  the  lungs  will  be 
doubled,  and  capable  of  supporting  the  system  twice  as  long  as  half  the 
quantity,  which  is  all  that  could  be  received  in  them  at  the  surface,  under 
the  ordinary  atmospheric  pressure. 

266.  Weight  of  Bodies  in  Air.— The  weight 
of  bodies  in  air  is  diminished  in  the  same 
manner  as  when  they  are  immersed  in  wa- 
ter (§  178),  though  the  loss  is  not  so  great 
in  consequence  of  the  lightness  of  air.  The 
weight  of  100  cubic  inches  of  air,  as  we  have 
seen,  is  a  little  more  than  31  grains;  conse- 
quently, (§  176),  when  a  body  is  weighed  in 
it,  it  will  be  sustained  to  this  amount  for 
every  hundred  cubic  inches  of  its  volume. 
That  is,  it  will  weigh  s*o  much  less  than  it 
would  in  a  vacuum,  making  no  allowance 
for  the  trifling  effect  of  the  air  in  sustaining 
the  weights  themselves.  Light  and  bulky 
substances  of  course  lose  much  more  in  pro- 
portion than  compact  heavy  ones.  This  is 
easily  shown  by  means  of  a  delicate  balance. 
Let  A,  figure  135,  be  a  hollow  sphere  of 
brass,  which  is  just  balanced  by  a  solid 
sphere  of  lead,  B,  when  in  the  open  air ;  then 
placing  them  thus  balanced  under  a  large  receiver,  exhaust 
the  air  by  means  of  the  air-pump,  and  the  larger  body,  A,  will 
be  seen  to  preponderate.  The  effect  will  be  the  same,  if,  in- 
stead of  the  hollow  sphere,  A,  a  piece  of  dry  sponge,  or  a  bunch 
of  cotton  or  feathers,  closely  tied,  be  used.  The  reason  is,  that 
the  larger  body,  displacing  more  air  than  the  smaller,  is  sus- 
tained more  by  it  than  the  smaller,  and  consequently  it  must 

air  in  the  bell  as  it  descends  ?  266.  Do  bodies  weigh  less  in  the  air  than 
they  would  in  a  vacuum  ?  What  is  the  weight  of  100  cubic  inches  of  air  ? 
Will  a  body  weighed  in  the  air  then  lose  31  grains  for  every  100  cubic  inches 
of  its  bulk  ?  Do  comparatively  light  or  heavy  bodies  lose  most  in  proportion 


Fig.  135. 


PNEUMATICS.  139 

be  really  heavier  in  order  that  an  equipoise  may  be  produced 
in  the  air;  and  when  the  air  is  removed,  the  heavier  body,  be- 
ing no  longer  supported,  will  of  course  preponderate.  From 
this,  it  will  be  seen,  the  common  method  of  weighing  is  not 
perfectly  accurate,  as  it  must  always  require  more  of  light  and 
bulky  articles,  as  wool,  feathers,  &c.,  to  make  a  pound,  than  it 
does  of  heavy  substances,  as  the  metals.  A  pound  of  feathers 
or  cotton,  therefore,  as  ordinarily  weighed,  must  always  be 
heavier  than  a  pound  of  lead.  In  order  that  the  pound  of  the 
two  substances  should  be  perfectly  equal,  it  would  be  necessary 
that  they  should  be  counterpoised  in  a  vacuum. 

267.  Balloons.  —  The  balloon,  or,  as  it  is  sometimes  called, 
the  air-balloon,  is  a  kind  of  vessel  designed  for  navigating  the 
air.     We  have  just  seen  that  bodies  in  the  air,  by  reason  of  its 
sustaining  power,  lose  a  part  of  their  weight ;  and  it  is  evident 
that,  if  a  body  of  sufficient  bulk  in  proportion  to  its  weight 
could  be  obtained,  it  would  rise  in  the  air  above  the  surface 
of  the  earth  in  the  same  manner  as  a  piece  of  wood  or  other 
light  substance  will  rise  in  water  when  held  at  a  distance  be- 
neath the  surface.    But,  unlike  the  piece  of  wood  in  water,  a 
body  of  this  kind  could  not  rise  and  float  upon  the  surface  of 
the  air  because  of  its  diminished  density  at  great  heights. 

268.  The  method  first  adopted  for  constructing  balloons  was 
to  obtain  large  vessels  from  which  the  air  might  be  exhausted, 
and  thus  their  weight  diminished,  while  the  bulk  remained  the 
same.   It  was  supposed  by  the  early  experimenters  that  hollow 
spheres  of  copper  might  be  made  sufficiently  light  for  this  pur- 
pose ;  but  it  has  been  found  by  trial  that  vessels  made  in  this 
manner  must  necessarily  be  so  weak  as  to  be  crushed  inward 
by  the  great  pressure  from  without,  as  soon  as  the  air  within 
is  exhausted. 

The  first  ascent  in  a  balloon  was  made  by  an  individual  in 
Paris  in  the  year  1783,  who  rose  to  the  height  of  3000  feet,  and 
descended  again  in  safety.  The  machine  which  he  used  con- 
sisted of  an  immense  elliptical  bag,  74  feet  long,  and  48  feet  in 
diameter,  filled  with  heated  air,  to  which  was  attached  a  kind 
of  basket,  made  of  wire,  to  contain  the  aeronaut.  Under  an 
aperture  at  the  bottom  of  the  bag  an  iron  grate  was  suspended 
containing  burning  fuel  to  maintain  the  rarefaction. 

when  weighed  in  the  air  ?  How  may  this  be  shown  by  experiment  ?  As 
ordinarily  weighed,  is  the  pound  of  cotton  or  feathers,  or  the  pound  of  lead 
heaviest  ?  267.  What  is  the  design  of  the  balloon  ?  What  is  necessary  in 
order  that  a  body  may  be  made  to  rise  in  the  air  ?  268.  What  was  the  me- 
thod first  adopted  for  constructing  balloons  ?  Can  hollow  spheres  of  metal 
be  made  so  as  to  be  at  the  same  time  sufficiently  strong  to  resist  the  external 
pressure  when  exhausted,  and  sufficiently  light  for  the  purpose  of  a  balloon  ? 
When  was  the  first  ascent  made  in  a  balloon  ?  How  was  the  balloon  used 
en  the  occasion  constructed  ?  How  may  small  balloons  of  paper  easily  be 
made  to  ascend  ?  What  will  be  the  effect  when  the  alcohol  is  consumed  ? 
Why  is  air  when  heated  lighter  than  when  cold  ? 


140 


NATURAL     PHILOSOPHY. 


Fig.  136. 


Small  balloons  made  of  paper  may  he 
easily  caused  to  ascend  to  a  considerable 
height  by  means  of  the  rarefaction  pro- 
duced by  burning  alcohol.  Let  A,  figure  1 36, 
be  a  spherical  bag,  4  feet  in  diameter,  made 
of  tissue-paper,  and  having  a  circular  open- 
ing at  the  lower  side,  B,  8  or  10  inches  in 
diameter.  In  the  centre  of  this  opening,  a 
piece  of  sponge,  saturated  with  alcohol,  is 
then  to  be  attached  by  means  of  small 
wires,  and  the  alcohol  inflamed.  As  the  air 
is  heated  by  the  flame,  it  expands  and  rises 
in  the  balloon,  inflating  it;  and,  when  a 
sufficient  quantity  has  accumulated,  causing  it  to  ascend  in  the 
air.  When  the  alcohol  is  consumed,  the  air  within  the  balloon 
is  soon  cooled,  and  it  again  descends  to  the  surface. 

The  cause  of  the  ascent  of  such  a  machine  is  easily  under- 
stood. Air,  when  heated,  as  just  intimated,  is  greatly  expanded, 
so  that  a  given  bulk  is  much  lighter  than  when  cold;  conse- 
quently, the  balloon,  with  the  sponge  and  alcohol,  when  filled 
with  heated  air,  is  lighter  than  the  same  bulk  or  volume  of  the 
surrounding  cold  air,  and  therefore  rises  through  it. 

269.  Large  balloons,  designed  to  ascend  any  considerable 
distance  above  the  surface,  are  now  usually  made  of  oiled  silk, 
and  inflated  with  hydrogen  gas,  which  is  admirably  adapted 
for  this  purpose,  being  about  14  times  lighter  than  air.  It  is 
indeed  the  lightest  substance  known  in  nature.  (For  mode  of 
preparing-  it,  $c.,  see  Author's  Chemistry,  page  150.) 

The  balloon  is  made  in  a  spherical  form, 
of  oiled  silk,  and  to  it  the  car,  made  as  light 
as  possible,  is  attached  by  numerous  cords 
drawn  over  it,  in  order  that  the  weight 
may  be  uniformly  sustained  by  every  part. 
Figure  137  represents  a  balloon  inflated, 
with  the  car  attached  to  it.  AB  is  the 
balloon,  with  the  network  drawn  over  it  to 
sustain  the  car;  C,  the  car;  and  PD,  the 
parachute,  resembling  a  large  umbrella. 
This  last  appendage  makes  no  necessary 
part  of  the  machine,  but  is  usually  added  in 
order  to  prevent  a  too  rapid  descent  of  the 
car,  should  it  by  any  accident,  as  some- 
times happens,  become  detached  from  the 
balloon,  or  should  any  accident  happen  to 
the  balloon  itself.  In  one  instance,  the  bal- 


Fig.  137. 


Quest.  269.  What  are  large  balloons  now  usually  made  of  ?  With  what 
are  they  inflated  ?  Why  is  this  substance  selected  ?  How  much  lighter  is  it 
than  air  ?  Of  what  form  is  the  balloon  made  ?  How  is  the  car  attached  to 
it  ?  What  is  the  parachute  ?  What  is  its  design  ?  Have  persons  descended 


PNEUMATICS.  141 

loon  being  detached  from  the  car  at  the  height  of  8000  feet,  the 
aeronaut,  by  means  of  his  parachute,  descended  in  safety. 

270.  As  the  atmosphere  diminishes  in  density  above  the  surface,  it  is 
evident  that  a  balloon  which  has  considerable  buoyancy  near  the  surface, 
if  its  volume  remains  the  same,  will  be  capable  of  rising  comparatively 
only  a  short  distance ;  but,  as  the  density  of  the  atmosphere  diminishes, 
the  pressure  diminishes  also;  and,  as  a  necessary  consequence,  as  the 
balloon  rises,  the  gas  within  it  expands.     To  prevent  danger  from  the 
bursting  of  the  balloon  by  this  expansion,  it  is  not  fully  inflated  at  first, 
but  gradually  becomes  so  as  it  ascends.     A  valve  opening  outward  is 
also  placed  in  the  top  to  allow  the  gas  to  escape  if  the  internal  pressure 
becomes  too  great. 

271.  The  greatest  height  to  which  balloons  have  been  made  to  ascend 
does  not  exceed  that  of  the  highest  mountains,  or  something  less  than  5 
miles;   At  elevations  much  less  than  this,  great  cold  is  always  experienced ; 
and  the  effects  of  the  diminished  pressure  upon  the  aeronaut  becomes  ap- 
parent by  the  quickening  of  the  pulse,  and  parching  of  the  throat,  and 
swelling  of  the  head. 

Birds  let  fall  from  great  heights,  it  is  said,  at  first  descend  almost  per- 
pendicularly,  their  wings  not  being  capable  of  sustaining  them  in  a  highly 
rarefied  atmosphere. 

The  impossibility  of  guiding  balloons  has  as  yet  prevented 
them  from  being  made  of  any  practical  use ;  they  can  be 
made  to  move  only  before  the  wind,  which  does  not  always 
blow  in  the  same  direction,  even  at  slight  elevations  above  the 
surface,  as  it  does  at  the  surface.  Hence,  if  the  aeronaut  delays 
until  the  wind  at  the  surface  is  in  the  proper  direction  to  make 
a  desired  passage,  on  ascending  a  little  he  may  find  it  blowing 
towards  a  different  point,  so  as  to  drive  him  far  from  his  ex- 
pected course.  Individuals  have,  however,  several  times  cross- 
ed the  channel  between  England  and  France,  but  not  without 
exposing  themselves  to  great  danger. 

272.  Attempts  were  made  under  Napoleon  to  render  balloons  useful  in 
military  operations,  by  enabling  a  sentinel  to  view  the  position  and  move- 
ments of  the  hostile  army  from  an  elevated  position.    When  used  for  this 
purpose,  the  balloon  was  inflated  and  secured  to  the  ground  by  a  rope  at 
such  an  elevation  as  was  desired,  and  signals  made  by  the  observer  to  the 
officers  below.    At  the  battle  of  Fleury,  a  French  general  ascended  in  this 
manner  to  the  height  of  nearly  1500  feet;  and  it  has  been  said  that  the 
information  he  was   able  to  communicate  to  his  commanding  officer, 
general  Jourdan,  by  means  of  signals,  decided  the  fate  of  the  contest. 

273.  Instead  of  hydrogen,  the  gas  prepared  from  bituminous  coal,  or 
from  resinous  or  oily  substances,  and  used  for  illuminating  purposes  in 
most  large  cities,  is  now  often  used  for  inflating  balloons,  in  consequence 
of  its  cheapness.  Though  much  lighter  than  air,  it  is  considerably  heavier 
than  hydrogen  ;  and  balloons  in  which  it  is  to  be  used,  in  order  to  ascend 
with  the  same  force,  must  be  made  larger  than  those  designed  for  hydro- 
gen gas.  (For  method  of  calculating  the  buoyancy  of  a  balloon,  see  Author's 
Chemistry,  page  154.) 

in  safety  from  great  heights  by  means  of  the  parachute  alone  ?  271.  What 
has  prevented  balloons  from  being  made  of  any  practical  use  ?  Does  the 
wind  always  blow  in  the  same  direction  above  the  surface,  as  it  does  at  the 
surface  ? 


142 


NATURAL     PHILOSOPHY, 


o 


274.  The  Steam-Engine.  —  The  steam-engine  is  a  machine 
for  producing  motion  by  the  elastic  force  of  steam  from  boiling 
water.  Though  it  is  an  instrument  of  great  power,  its  inven- 
tion is  comparatively  very  recent;  indeed,  it  has  only  been 
brought  to  a  state  of  perfection  (if  so  much  can  even  now  be 
said  of  it)  within  the  last  few  years. 

Water  boils,  or  is  converted  into  steam,  as 
is  well  known,  whenever  it  is  heated  to  212° 
of  Fahrenheit's  thermometer;  and  the  steam 
formed  from  any  given  quantity  of  water 
occupies  1696  times  as  much  space  as  the 
water  itself.  Consequently,  if  a  vessel  capa- 
ble of  being  closed  air-tight  be  nearly  filled 
with  water,  and  heat  applied  so  as  to  convert 
it  into  steam,  it  will  fill  the  whole  vessel,  and 
unless  it  is  very  strong,  will  burst  it  outward. 
If  a  small  orifice  is  made  above  the  surface 
of  the  water  within  for  its  escape  into  the  air, 
a  jet  of  steam  will  issue  from  it  with  great 
force.  If  to  this  orifice  a  cylindrical  tube  is 
attached,  containing  a  solid  piston  and  rod, 
the  piston  will  be  forced  out  before  the  steam, 
carrying  with  it  whatever  may  be  attached 
to  the  rod.  This  may  be  illustrated  by  figure 
138.  ABC  is  a  large  glass  flask  or  matrass, 
having  a  long  cylindrical  neck,  B  C,  of  as 
equal  a  diameter  in  every  part  of  its  length 
as  possible.  The  bulb  or  body  of  the  vessel, 
A,  is  to  be  partly  filled  with  water,  and  the 
piston,  P,  inserted  by  means  of  the  rod  and 
handle  attached  to  it.  If  now  a  lamp  is  placed 
under  A,  the  water  will  soon  be  made  to  boil, 
and  sufficient  steam  be  formed  to  force  up 
the  piston  quite  to  the  top  of  the  tube.  But, 
if  the  lamp  is  removed,  no  more  steam  will 
be  formed ;  and  that  within  will  soon  begin  to  be  condensed 
into  water  by  the  cold  air  surrounding  the  outside  of  the  vessel, 
producing  a  vacuum,  and  leaving  the  piston  to  be  forced  down 
again  by  the  pressure  of  the  atmosphere.  If  a  little  cold  water 
is  sprinkled  upon  the  bulb,  A,  above  the  water,  the  steam  will 
be  condensed  much  sooner,  and  the  piston  of  course  descend 

Quest.  274.  What  is  the  steam-engine  ?  Is  its  invention  of  recent  date  ? 
At  what  temperature  does  water  boil  ?  How  many  times  is  the  bulk  of 
water  expanded  in  changing  into  steam  ?  How  may  steam  be  made  to  issue 
from  a  vessel  with  great  force  ?  If  a  straight  tube  containing  a  solid  piston 
is  connected  with  the  vessel  of  boiling  water,  what  will  be  the  effect  ?  How 
is  this  illustrated  by  figure  138  ?  What  will  be  the  effect  if  the  lamp  is  re- 
moved ?  What  will  be  the  effect  of  sprinkling  a  little  cold  water  upon  the 
vessel  above  the  surface  pf  the  water  ?  How  may  the  piston  be  made  to  rise 
again? 


Fig.  138. 


PNETJ  M ATICS 


143 


more  rapidly.    By  applying  the  lamp  again,  the  piston  may  of 
course  be  forced  up  as  before. 

275.  In  order  to  understand  this  fully,  it  is  necessary  only  to 
observe  that,  as  water  is  converted  into  steam  by  raising  its 
temperature  to  212  degrees,  so,  if  steam  already  formed  has  its 
temperature  reduced  below  this  point,  it  will  be  again  con- 
verted into  water ;  and  if,  in  the  first  instance,  its  volume  was 
increased  1696  times,  so  also  in  the  second  it  must  be  diminish- 
ed in  the  same  ratio. 

In  this  simple  apparatus,  A  may  be  considered  the  boiler, 
and  the  tube,  B  C,  the  cylinder,  as  these  terms  are  used  in  re- 
ference to  the  steam-engine. 

It  is  very  evident  that  an  engine  constructed  after  this  model 
would  accomplish  but  little,  as  its  motion  must  necessarily  be 
slow,  the  piston  being  urged  in  one  direction  only  by  the 
steam,  and  in  the  other  direction  by  atmospheric  pressure.  In 
the  steam-engine,  as  now  used,  the  steam  is  let  into  the  cylin- 
der on  both  sides  of  the  piston,  its  action  being^  entirely  inde- 
pendent of  atmospheric  pressure. 

276.  There  are  two 
kinds  of  the  steam- 
engine,  the  high-pres- 
sure engine,  "as  it  is 
called,  and  the  low- 
pressure  engine.  We 
will  first  give  an  ex- 
planation of  the  es- 
sential parts  of  the 
former,  or  high-pres- 
sure engine.  As  the 

k. machine,  with  all  its 

appendages,  is  neces- 
sarily very  complex, 
we  shall  find  it  for 
our  advantage  to 
confine  our  attention 
exclusively  to  the 
parts  necessary  to 
produce  motion,  ar- 
ranged not  as  they 
are  found  in  working 


Fig.  139. 


engines,  but  in  such  a  manner  that  they  can  be  conveniently 
represented  on  paper.  Figure  139  is  designed  to  represent  a 
section  of  a  boiler,  and  cylinder  with  its  piston,  steam-pipes, 

Quest.  275.  What  effect  is  produced  upon  steam  if  cooled  below  212°? 
What  part  of  the  apparatus,  figure  138,  may  be  considered  the  boiler,  and 
what  the  cylinder  ?  Would  an  engine  constructed  after  the  above  model  be 
effective  ?  276.  What  two  kinds  of  the  steam-engine  are  there  ?  In  figure 
139,  what  is  the  boiler,  and  what  the  cylinder  and  piston  ?  How  are  the 


144  NATURAL     PHILOSOPHY. 

and  valves.  B  is  a  section  of  the  boiler  partly  filled  with  water ; 
AD  the  cylinder;  Q,  the  piston;  R  with  the  rod  which  plays 
through  the  collar,  so  as  to  be  steam-tight.  A  steam-pipe,  S, 
passes  from  the  upper  part  of  the  boiler,  and  branching  into  two 
parts,  connects  with  the  cylinder  at  the  top  and  bottom.  Another 
pipe  is  placed  on  the  opposite  side  of  the  cylinder,  connecting 
also  with  it  at  the  top  and  bottom,  called  the  escape-pipe,  having 
an  opening  at  T.  M  N  O  and  P  are  valves  which,  for  our  pur- 
pose, we  will  suppose  to  be  opened  arid  shut  by  the  hand,  as 
occasion  may  require.  C  is  a  safety-valve,  which  is  kept  closed 
by  a  weight  attached  to  a  lever.  It  is  designed  to  prevent  dan- 
ger by  the  bursting  of  the  boiler  from  a  too  great  accumulation 
of  steam  within.  When  the  pressure  has  increased  to  a  certain 
point,  this  valve  is  lifted  by  it,  and  the  steam  makes  its  escape. 

277.  Now,  suppose  the  fire  to  be  kindled  under  the  boiler, 
and  the  space  above  the  water  filled  with  steam,  which  will 
find  its  way  along  the  steam-pipe  to  the  valves  M  and  N ;  if 
the  valves  N  and  O  are  now  opened  simultaneously,  the  steam 
will  rush  into  the  lower  part  of  the  cylinder,  and  by  its  elastic 
force  raise  the  piston,  at  the  same  time  driving  out  the  air 
above  it  through  the  valve,  O,  and  aperture,  T.     When  the 
piston  has  reached  the  top  of  the  cylinder,  the  valves  N  and  O 
are  to  be  closed,  and  M  and  P  at  the  same  time  opened ;  the 
steam  from  the  boiler  will  then  pass  into  the  cylinder  above 
the  piston,  forcing  it  down,  that  below  it  escaping  by  the  valve, 
P,  and  aperture,  T,  as  before.     To  cause  the  piston  again  to 
ascend,  the  valves,  M  and  P  are  to  be  closed,  and  N  and  O  at 
the  same  time  opened ;  thus,  a  reciprocating  motion  of  the 
piston  is  produced  through  the  length  of  the  cylinder,  by  open- 
ing and  closing  two  valves  at  each  stroke.     The  force  with 
which  the  piston  will  move  will  depend  upon  the  amount  of 
pressure  of  the  steam  upon  a  square  inch,  and  upon  the  dia- 
meter of  the  cylinder. 

We  have  here  supposed  the  valves  to  be  opened  and  closed 
by  hand— and  this  was  the  method  actually  adopted  in  the  first 
steam-engines — but  this  is  now  accomplished  by  the  action  of 
the  machinery  itself. 

278.  It  will  be  observed,  too,  that  the  escape-pipe  opens 
directly  into  the  air,  so  that  the  steam,  after  having  produced 
its  effect,  is  forced  out  at  T,  against  the  pressure  of  the  atmo- 
sphere.    Consequently,  the  pressure  of  the  steam  in  the  boiler, 
in  order  to  move  the  piston,  must  be  more  than  equivalent  to 

boiler  and  cylinder  connected  ?  Why  does  this  pipe  branch  into  two  parts  ? 
What  is  the  escape-pipe  ?  What  is  the  design  of  the  safety-valve  ?  277. 
Supposing  the  steam  to  be  raised,  how  may  the  piston  be  forced  up  to  the 
upper  part  of  the  cylinder  ?  How  may  it  be  again  forced  down  ?  What  now 
is  necessary  to  give  the  piston  a  constant  reciprocating  motion  ?  Are  the 
valves  always  opened  and  closed  by  hand  ?  278.  Into  what  does  the  steam 
escape  in  this  engine  ?  Must  the  pressure  of  the  steam  in  the  boiler,  there- 


PNEUMATICS. 


145 


the  ordinary  atmospheric  pressure ;  hence,  an  engine  of  this 
construction  is  called  a  high-pressure  engine,  in  contradistinc- 
tion from  the  low-pressure  engine,  in  which  the  escape-pipe 
opens  into  a  vessel  of  cold  water  called  the  condenser,  as  will 
shortly  be  described. 

279.  Figure  140  is  a 
section  of  the  cylinder, 

B,  condenser,  air-pump, 

&c.,  of  a  low-pressure 
steam-engine.  All  the 
parts  immediately 
connected  with  the 
cylinder  are  precisely 
the  same  as  in  the 
,  high-pressure  engine ; 
but  the  escape-ptpe  at 
T,  instead  of  opening 
into  the  air,  enters  a 
large  cistern  1,  2,  3,  4, 
which  is  kept  filled 
with  cold  water,  arid 
is  there  considerably 
enlarged.  GH  is  an 
air-pump,  connected 
3  with  the  escape-pipe 
by  a  large  tube  and 
valve.  At  V  is  a  short 
tube  with  a  faucet  by  which  water  is  admitted  from  the  cistern 
to  condense  the  steam  as  it  enters  from  the  escape-pipe,  T.  As 
a  vacuum  is  always  kept  up  in  the  condenser  by  the  air-pump, 
the  cold  water  will  of  course  rush  in  by  atmospheric  pressure. 
It  will  now  be  easy  for  the  intelligent  student  to  understand 
the  construction  and  the  mode  of  action  of  this  engine,  and  in 
what  it  differs  from  the  high-pressure  engine.  The  air-pump 
is  worked  by  the  engine  itself;  it  is  called  an  air-pump  because 
the  design  of  it  is  to  keep  up  a  vacuum  in  the  condenser  by 
exhausting  the  air  at  first  contained  in  it,  and  any  that  may 
enter  with  the  steam  or  with  the  water  from  the  injection-pipe 
V.  It  also  removes  the  water  that  enters  by  the  injection-pipe, 
which  is  allowed  to  escape  by  the  pipe  at  G. 

fore,  be  always  greater  than  the  ordinary  pressure  of  the  atmosphere  ?  Into 
what  does  the  steam  escape  in  the  low-pressure  engine  ?  Whafis  the  essen- 
tial difference  between  the  high  and  low  pressure  engine  ?  279.  Are  the 
boiler,  cylinder,  piston,  &c.,  the  same  in  both  the  high  and  low  pressure 
engines  ?  Into  what  does  the  escape-pipe  lead  in  figure  140  ?  What  is  the 
use  of  the  air-pump  in  this  engine  ?  How  is  the  water  made  to  enter  the 
condenser  ?  How  is  the  air-pump  worked  ?  How  is  the  water  removed 
from  the  condenser  ? 

13 


Fig.  140. 


246  NATURAL     PHILOSOPHY. 

280.  There  are  in  the  perfect  engine  several  other  parts  not 
here  represented,  as  a  cold-water  pump,  to  keep  the  cistern 
1,  2,  3,  4,  constantly  supplied;  and  also  a  hot- water  pump, 
which  takes  a  portion  of  the  water  that  has  passed  through  the 
condenser,  and  forces  it  into  the  boiler,  in  which  the  water 
must  be  kept  at  nearly  a  uniform  height.    These  parts,  as  well 
as  those  represented  in  the  figure,  though  always  performing 
the  same  office,  are  often  variously  constructed  and  differently 
situated,  as  convenience  in  particular  cases  or  caprice  may 
dictate. 

281.  The  manner  in  which  a  rotary  motion  is  communicated 
to  a  wheel  by  the  reciprocating  motion  of  the  piston-rod,  may 
be  readily  conceived  by  noticing  the  common  itinerant  knife- 
grinder  turning  his  grindstone   by  means  of  a  treadle  and 
crank.    Putting  the  stone  first  in  the  proper  position  by  the 
hand,  by  a  downward  motion  of  the  treadle  and  crank,  it  be- 
gins to  revolve;  and  as  soon  as  the  crank  has  reached  its 
lowest  point,  by  lifting  the  foot,  the  revolving  motion  is  con- 
tinued by  the  mere  momentum  of  the  parts  until  half  a  revolu- 
tion is  made,  and  the  crank  is  in  the  proper  position  again  for 
a  new  impulse  to  be  given  it  by  a  second  downward  motion 
of  the  treadle,  as  before.     By  properly  managing  the  motions 
of  the  foot,  a  great  velocity  may  be  given  to  the  stone,  even 
though  considerable  resistance  is  to  be  overcome. 

In  the  case  of  the  knife-grinder,  the  propelling  power  can 
have  but  a  single  downward  motion,  and  can  act  only  through 
half  a  revolution  of  the  stone ;  but  if,  instead  of  the  foot,  a  rod 
is  used,  attached  by  a  hinge-joint  to  the  piston-rod  of  a  steam- 
engine,  an  impulse  can  be  given  both  upward  and  downward, 
by  which  a  much  greater  resistance  can  be  overcome,  and 
steadiness  of  motion  secured.  There  must,  however,  always 
be  two  points,  called  the  dead-points,  by  which  the  revolutions 
must  be  continued  by  the  momentum  of  the  machinery.  To 
ensure  steadiness  of  motion  in  every  part  of  a  revolution  of 
the  crank,  a  large  heavy  wheel,  called  a  fly-wheel,  is  often  at- 
tached, especially  in  small  engines,  in  which  the  parts  of  the 
engine  itself  have  but  a  small  momentum. 

For  a  more  full  description  of  this  instrument  of  human 
power,  the  reader  is  referred  to  larger  works  devoted  to  the 
subject,  especially  Professor  Renwick's  recent  lucid  treatise  on 
the  Steam-Engine. 

Quest.  280.  What  is  the  use  of  the  cold-water  pump  ?  What  is  the  use 
of  the  hot- water  pump  ?  Are  the  parts  of  the  engine  described  always 
constructed  in  the  same  manner  ?  281 .  How  is  a  rotary  motion  produced 
by  means  of  the  engine  which  gives  directly  only  a  reciprocating  motion 
backward  and  forward  ?  How  does  the  knife-grinder  turn  his  grindstone  by 
means  of  a  treadle  ?  In  the  case  of  the  knife-grinder,  does  the  propelling 
power  act  in  more  than  one  direction  ?  In  the  steam-engine,  in  what  direc- 
tions is  the  impulse  given  ?  What  is  the  use  of  the  fly-wheel  ? 


PNEUMATICS. 


14? 


Fig,  141, 


282.  The  Rotary  Steam-Engine^  which  has  been  used 
with  some  success,  acts  on  a  principle  entirely  different 
from  the  preceding.  It  has  been  constructed  in  different 
modes,  but  th*  principle  of  its  action  may  be  understood 
from  figure  141,  which  represents  a  toy  made  by  com- 
mon glass-blowers.  Bis  a  globular  vessel  of  thin  glass, 
which  rests  upon  a  pivot,  A,  and  is  supported  by  a 
stand.  From  opposite  sides  of  the  vessel,  at  its  upper 
part,  two  tubes  proceed,  and  near  their  extremities  are 
bent  nearly  at  right-angles  in  opposite  directions.  If, 
now,  a  little  water  is  poured  into  the  vessel,  and  heat 
applied  by  means  of  a  lamp,  the  steam,  as  it  is  formed, 
on  escaping  from  the  tubes,  will  give  it  a  rapid  rotatory 
motion.  The  steam,  as  it  issues  from  the  tube,  meets 
with  resistance  from  the  air ;  but  the  current,  being- 
urged  on  by  the  pressure  within,  puts  the  tube  in  mo- 


ffion  in  the  opposite  direction.  A  current  of  water  issuing  from  an  orifice 
produces  the  same  effect ;  and  it  is  on  this  principle  that  Barker's  centri- 
fugal mill  is  constructed. 

Rockets  are  propelled  through  the  air  by  means  of  a  current  of  heated 
gas  issuing  in  this  manner  fivm  a  tube.  A  kind  of  gun-powder  (if  it  is 
proper  so  to  call  it)  is  made,  that  burns  much  slower  than  that  usually 
seen ;  and  a  tube  of  strong  paper  is  filled  with  it,  and  one  end  inflamed; 
and  the  rocket  shoots  rapidly  into  the  air  by  means  of  the  current  of  heated 
g-as  that  is  produced  and  rushes  out  from  the  tube.  A  long  slender  stick 
is  usually  attached  to  it,  to  direct  it  in  its  course, 

283.  Meteorology.  —  Meteorology  is  the  branch  of  science 
which  treats  of  the  various  phenomena  of  the  atmosphere,  as 
heat,  cold,  rain,  snow,  haiJ,  clouds,  winds,  &c.  The  tempera- 
ture of  the  atmosphere  is  exceedingly  different  in  different 
parts,  even  though  in  the  immediate  vicinity  of  each  other. 
As  a  general  rule,  admitting  of  few  exceptions,  the  strata 
nearest  the  earth  are  warmest;  and,  as  we  ascend,  a  gradual 
reduction  of  temperature  is  observed  to  the  highest  point  that 
lias  been  attained  by  man.  The  reason  of  this  probably  is  in 
part  because  the  air  receives  its  heat  chiefly  if  not  wholly  from 
the  earth ;  the  rays  from  the  sun  pass  through  it,  as  they  do 
through  glass  or  other  transparent  media,  without  affecting  its 
temperature;  but,  being  received  and  absorbed  by  the  earth,  a 
portion  is  again  imparted  to  the  atmosphere,  of  course  heating 
its  lower  strata  first.  Another  cause  is  found  in  the  fact,  that, 
as  any  portion  of  air  ascends  above  the  surface,  a  great  ex- 
pansion takes  place  by  reason  of  the  diminished  pressure  to 
which  it  is  subject;  and  this  it  is  well  known  is  always  attend- 
ed by  a  reduction  of  temperature.  As  the  strata  near  the  earth 
are  warmer  than  those  above,  it  might  be  expected  that  they 

Quest.  283.  What  is  meteorology  ?  Is  the  temperature  of  the  atmosphere 
the  same  in  every  part  ?  From  wh'at  does  the  air  chiefly  receive  its  heat  ?  Do 
the  rays  of  heat  from  the  sun  generally  pass  through  transparent  bodies 
without  heating  them  ?  How  is  Ihe  temperature  of  a  portion  of  air  affected 
as  it  rises  above  the  surface  ?  When  the  air  near  the  surface  becomes  heated. 


148  NATURAL     PHILOSOPHY* 

N 

would  rise  and  give  place  to  the  colder  portions,  according  to 
the  general  law  of  fluids  in  such  cases*— and  this  to  a  certain 
extent  undoubtedly  does  take  place— but  while  the  lower  strata 
are  warmer  than  those  above,  they  are  at  the  same  time  under 
greater  pressure,  and  may  therefore  be  more  dense.  If  the 
temperature  of  the  lower  strata  is  raised  above  a  certain  point, 
they  become  so  rarefied,  notwithstanding  the  greater  pressure 
to  which  they  are  subjected,  as  to  rise  and  give  place  to  sur- 
rounding colder  portions, 

As  the  cold  increases  in  proportion  as  we  ascend  above  the 
surface,  it  is  evident  a  point  may  be  attained,  above  which, 
even  on  the  equator,  ice  and  frost  will  remain  during  the  whole 
year.  This  is  called  the  altitude  of  perpetual  congelation.  This 
is  found  by  observation  to  be  on  the  equator  about  15,600  feet 
above  the  level  of  the  sea ;  at  20  degrees  from  the  equator  it 
takes  place  at  the  height  of  a  little  more  than  13,700  feet;  and 
45  degrees  from  the  equator  at  about  7658  feet ;  while  at  the 
poles,  and  indeed  at  some  distance  from  them,  ice  remains 
during  the  year  upon  the  surface  of  the  sea. 

But  it  is  often  found  that  different  strata  of  air,  immediately 
adjacent  to  each  other,  are  at  very  different  temperatures. 
Thus,  the  aeronaut  in  ascending,,  often  passes  suddenly  from 
a  warm  to  a  very  cold  region,  where  snow  and  hail  are  form- 
ing; but,  on  rising  higher,  it  becomes  warmer  again.  This,  no 
doubt,  is  occasioned  by  local  currents  in  the  atmosphere,  by 
which  portions  of  the  air  of  different  latitudes,  and  perhaps 
distant  places,  are  brought  into  the  immediate  vicinity  of  each 
other. 

284.  Wind  is  moving  air,  and  is  occasioned  generally,  it  is 
supposed,  by  changes  of  temperature  in  different  regions  of 
the  atmosphere.  When  the  air  in  a  particular  district  becomes 
heated  above  that  in  surrounding  parts,  it  rises,  and  the  colder 
air  in  the  vicinity  rushes  in  to  supply  its  place.  This  is  well 
illustrated  by  the  phenomena  attending  the  kindling  of  a  large 
fire  in  the  open  air  in  calm  weather.  By  passing  around  the 
fire,  it  will  be  observed  that  the  wind  blows  towards  it  on 
every  side ;  while  above  it  a  current  sets  upward  with  so  much 

will  it  always  rise  and  give  place  to  surrounding  cdder  portions  ?  How  does 
the  temperature  change  as  we  ascend  from  the  surface  ?  What  is  meant  by 
the  altitude  of  perpetual  congelation  ?  What  is  this  altitude  on  the  equator  ? 
What  is  it  at  20  degrees  from  the  equator  ?  What  is  it  at  the  distance  of  45 
degrees  ?  And  what  at  the  poles  ?  Are  the  strata  of  air  immediately  adja- 
cent to  each  other  at  different  temperatures  ?  What  is  often  observed  by  the 
aeronaut  as  he  ascends  in  his  balloon  through  different  strata  of  the  air  ? 
How  may  the  occurrence  of  different  strata  in  this  manner  be  accounted  for  ? 
284.  What  is  wind  ?  How  is  the  motion  of  the  air  occasioned  ?  What 
effect  is  produced  when  the  air  in  a  particular  district  becomes  heated  above 
that  of  surrounding  regions  ?  How  is  this  illustrated  ? 

*  See  Author's  Chemistry,  page  20. 


PNEUMATICS.  14$ 

force  that  fragments  of  the  burning  materials  are  often  car- 
ried up  to  considerable  heights.  The  accidental  burning  of  a 
building  in  a  calm  evening  sometimes  affords  an  opportunity 
of  witnessing  these  effects  in  the  most  striking  manner. 

285.  The  rise  of  smoke  in  a  chimney,  and  the  current  of  air 
produced  in  the  pipe  leading  from  a  stove,  are  dependent  upon 
the  same  cause.    The  air  being  heated  by  the  fire  and  expand- 
ed, becomes  lighter  than  the  surrounding  atmosphere,  and 
therefore  rises  often  with  considerable  force.     Before  a  fire, 
near  the  floor,  a  current  will  always  be  found  setting  towards 
the  fire  to  supply  the  place  of  that  which  is  constantly  ascending 
in  the  chimney.  The  same  will  be  observed  of  the  air  in  front  of 
a  stove;  but  only  a  slight  current  will  in  this  case  be  discovered, 
since  the  quantity  of  air  that  passes  up  the  chimney  is  much 
less  than  when  an  open  fireplace  is  used.     We  see  therefore 
why  the  same  quantity  of  fuel  will  heat  a  room  much  more 
when  burned  in  a  close  stove  than  when  an  open  fireplace  is 
used;  in  the  latter  case  no  more  air  is  allowed  to  enter  the 
stove  and  pass  up  the  chimney  than  is  necessary  for  the  com- 
bustion of  the  fuel ;  but  when  an  open  fireplace  is  used,  much 
heated  air  from  the  room  escapes  with  the  gases  and  smoke 
produced  by  the  combustion.     Of  course  as  much  of  cold  air 
must  always  enter  a  room  as  there  is  of  warm  air  that  escapes; 
and  thus  a  large  proportion  of  the  fuel  is  expended  to  no  use- 
ful purpose. 

We  see  here,  too,  why  the  chimney  of  a  new  close  room  is 
likely  to  smoke.  In  order  that  a  strong  current  may  be  formed 
in  the  chimney,  it  is  evident  a  good  supply  of  air  must  be  ad- 
mitted from  without ;  but,  if  this  is  prevented  by  the  closeness 
of  the  room,  the  current  in  the  chimney  cannot  be  formed,  and 
as  a  necessary  consequence,  the  smoke,  instead  of  passing  out 
by  the  chimney,  rises  in  the  room.  When  this  is  the  case,  a 
perfect  remedy  is  usually  found  in  opening  some  door  of  the 
apartment  by  which  a  good  supply  of  air  is  admitted. 

286.  The  land  and  sea  breezes  which  daily  occur  on  the  coast 
and  in  the  islands  of  the  tropical  regions,  are  produced  in  a 
similar  manner,  but  on  an  immensely  larger  scale.     In  some 
of  the  West  India  islands  they  occur  with  great  regularity. 
About  9  o'clock,  A.M.,  the  wind  begins  to  blow  from  the  sea 

Quest.  285.  What  occasions  the  rise  of  the  smoke  in  a  chimney  and  the 
pipe  of  a  stove  ?  In  what  direction  does  the  air  move  near  the  floor  before,  an 
open  fire  in  a  room  ?  Is  the  current  as  perceptible  before  a  close  stove  ? 
What  is  the  reason  ?  Why  will  not  the  burning  of  a  given  quantity  of  fuel 
in  an  open  fireplace  heat  a  room  as  much  as  if  it  were  burned  in  a  close 
stove  ?  How  is  the  place  of  the  air  supplied  that  escapes  through  the  chim- 
ney ?  Why  is  the  chimney  of  a  new  close  room  likely  to  smoke  ?  Why  ig 
the  difficulty  remedied  usually  by  opening  a  door  ?  286.  How  are  the  land 
and  sea  breezes  of  the  West  Indies  and  other  tropical  climates  produced  ? 
At  what  hours  do  these  breezes  commence  ?  How  are  these  winds  accounted 
13* 


150  NATURAL     PHILOSOPHY. 

towards  the  land  on  every  side  of  the  islandr  and  continues 
until  evening,  when  after  a  period  of  calm  it  commences  to 
blow  from  the  land  in  all  directions  towards  the  sea.  The 
former  is  called  the  sea,  and  the  latter  the  land-breeze.  They 
are  occasioned  by  the  unequal  effect  of  the  sun's  rays  on  the 
land  and  water,  the  latter  being  heated  or  cooled  much  less 
readily  than  the  former.  The  action  of  the  sun's  rays  in  the 
morning  soon  raises  the  temperature  of  the  land  above  that 
of  the  neighbouring  ocean ;  and  a  portion  of  the  heat  being 
communicated  to  the  air  above  it  causes  it  to  ascend  as  before 
explained,  and  the  air  from  the  surrounding  water  rushing  in 
to  supply  its  place,  produces  the  regular  sea-breeze.  After 
sunset,  the  land  (with  the  air  above  it)  cooling  more  rapidly 
than  the  water,  the  latter  soon  becomes  warmest,  and  a  current 
of  air  is  established  in  the  opposite  direction  from  that  in  the 
morning,  or  from  the  land  towards  the  sea,  which  constitutes 
the  land-breeze. 

287.  In  some  parts  of  the  Indian  Ocean,  from  November  to 
March,  the  wind  generally  blows  from  the  north-east  to  the 
south-west;   and  from  March  to  November  in  the  opposite 
direction,  from  south-west  to  north-east.     These  winds  are 
called  monsoons;  their  cause  is  not  well  understood,  but  no 
doubt  it  is  in  part  at  least  to  be  attributed  to  the  unequal  dis- 
tribution of  the  sun's  heat  over  the  surface  during  the  different 
seasons  of  the  year.    It  will  be  observed  that  the  general  direc- 
tion of  the  wind  is  from  the  north  of  the  equator  towards  the 
south,  during  that  part  of  the  year  in  which  the  heating  influ- 
ence of  the  sun's  rays  is  greatest  at  the  south ;  and  in  the  op- 
posite direction  during  the  part  of  the  year  when  the  sun's 
heat  is  greatest  at  the  north.  This  would  seem  to  indicate  that 
the  rarefying  influence  of  the  sun's  rays  is  a  great,  though  not 
perhaps  the  sole  cause  of  the  phenomenon. 

288.  The  same  cause,  it  is  very  well  ascertained,  produces 
the  trade-winds,  which  blow  constantly  from  a  general  easterly 
direction  some  28  or  30  degrees  north  and  south  from  the 
equator  in  the  Atlantic  and  Pacific  Oceans.  North  of  the  equa- 
tor they  are  found  to  vary  from  the  east  to  the  north-east,  and! 
in  like  manner,  south  of  the  equator,  their  general  direction  is 
from  the  south-east ;  but  in  both  hemispheres  they  are  subject 
to  some  variation,  according  to  the  season  of  the  year,  and  are 
affected  often  by  the  proximity  of  land.  By  the  diurnal  motion 
of  the  earth,  those  parts  of  its  surface  exposed  to  the  sun's 

for?  Why  is  the  air  over  the  land  heated  and  cooled  more  readily  than  that 
over  the  water  ?  287.  Where  do  the  winds  called  the  monsoons  occur  ?  In 
what  directions  do  they  blow  from  March  to  November,  and  from  Novem- 
ber to  March  ?  To  what  are  these  winds,  in  part  at  least,  to  be  attributed  ? 
238.  In  what  direction  do  the  trade-winds  constantly  blow  ?  North  of  the 
equator,  in  what  direction  do  they  vary  ?  In  what  direction  do  they  vary 
south  of  the  equator  ?  Are  they  modified  by  the  proximity  of  land  ?  In  what 


PNEUMATICS.  151 

more  direct  rays  become  heated  above  the  adjacent  parts,  pro- 
ducing a  disturbance  in  the  equilibrium  of  the  air  above  them, 
in  the  same  manner  as  already  pointed  out.  As  the  point  of 
greatest  heat  is  constantly  progressing  west  with  great  rapidity, 
it  is  followed  by  a  current  of  air  setting  towards  it,  though,  as 
we  should  expect,  on  the  north  of  the  equator,  inclining  more 
or  less  from  the  northward,  and  on  the  south  of  the  equator, 
from  the  southward.  Above  the  regions  where  the  trade-winds 
prevail,  it  has  been  very  satisfactorily  ascertained,  there  are 
currents  of  air  in  the  opposite  directions  from  the  winds  at  the 
surface ;  that  is,  while  the  currents  of  air  at  the  surface  move 
in  a  general  direction  from  east  to  west,  in  the  upper  regions 
of  the  atmosphere  they  are  moving  in  a  general  direction  from 
west  to  east.  Thus,  when  volcanic  eruptions  have  occurred  in 
some  of  the  West  India  islands,  ashes  thrown  out  have  been 
known  to  fall  far  to  the  eastward,  though  the  wind  at  the  sur- 
face all  the  time  was  blowing  from  that  direction. 

The  trade- winds  north  and  south  of  the  equator  do  not  meet, 
as  might  be  supposed ;  but  there  is  a  space  of  some  200  or  300 
miles  between  them,  called  the  region  of  calms,  where  there  is 
seldom  any  wind.  This  fact  entirely  refutes  the  notion  which 
formerly  prevailed,  that  these  winds  are  occasioned  merely  by 
the  motion  of  the  earth  on  its  axis ;  as  the  atmosphere,  though 
it  partakes  of  the  motion  of  the  earth,  might  be  supposed  to 
move  less  rapidly  than  the  earth,  and  therefore,  to  persons  on 
the  surface,  have  the  appearance  of  moving  in  the  contrary- 
direction,  or  from  east  to  west.  On  this  supposition,  it  is  evi- 
dent the  wind  should  be  strongest  at  the  equator,  where  the 
motion  of  the  earth  is  greatest,  contrary  to  what  has  just  been 
shown  to  be  the  fact. 

289.  Whirlwinds  are  violent  movements  of  the  atmosphere, 
in  a  circular  or  spiral  direction  about  an  axis,  the  whole  having 
at  the  same  time  a  progressive  motion.  They  occur  chiefly  in 
the  tropical  regions,  but  extend  also  into  the  temperate  zones. 
Sometimes  they  are  of  very  limited  extent ;  at  others  they  ex- 
tend over  a  portion  of  the  surface  included  in  a  circle  of  several 
hundred  miles  in  diameter.  They  then  constitute  the  tornados 
of  the  Atlantic  ocean  and  West  Indies,  and  typhoons  of  the 
Chinese  sea.  In  the  western  part  of  the  Atlantic  ocean,  it  is 
found,  they  usually  commence  in  the  vicinity  of  the  West  In- 
dies, and  progress,  with  greater  or  less  rapidity,  along  the 

direction  does  the  point  on  the  surface  of  the  earth,  when  the  heating  influ- 
ence of  the  sun's  rays  is  greatest,  constantly  move  ?  In  what  direction  do  the 
currents  of  air  move  in  the  upper  regions  of  the  atmosphere  in  those  parts  of 
the  earth  where  the  trade-winds  prevail  ?  How  has  this  been  ascertained  ? 
Do  the  trade-winds  blow  at  the  equator  ?  May  the  constant  easterly  direc- 
tion of  the  winds  between  the  tropics  be  occasioned  by  the  diurnal  motion  of 
the  earth  ?  On  this  supposition,  where  should  the  trade-winds  be  strongest  ? 
289.  What  are  whirlwinds  ?  Where  do  they  chiefly  occur  ?  What  is  said 
of  their  extent  ?  What  are  tornados  ?  What  are  they  called  when  they 
occur  in  the  Chinese  sea  ?  Where  is  it  found  they  usually  commence  in  the 


152  NATURAL    PHILOSOPHY. 

coast  of  the  United  States,  towards  the  north,  until  they  are 
dissipated  or  lost  in  high  northern  latitudes.  North  of  the 
equator,  the  whirl,  it  is  believed,  is  always  in  the  direction  of 
the  points  of  the  compass,  N.  W.  S.  and  E. ;  while  south  of  the 
equator  they  are  in  the  opposite  direction,  or  from  N.  through 
the  E.  S.  and  W. 

290.  The  atmosphere,  it  is  well  known,  even  when  dryest, 
always  contains  in  it  a  portion  of  watery  vapour,  from  which 
dew,  fog,  clouds,  rain,  snow,  hail,  &c.,  are  formed.  This  va- 
pour is  constantly  rising  from  the  surface  at  every  temperature, 
but  its  formation  is  much  the  most  rapid  in  warm  weather, 
and  the  atmosphere  then  contains  the  most  moisture.  Its  pre- 
sence is  shown  whenever  a  pitcher  is  filled  with  cold  spring- 
water,  and  allowed  to  stand  a  short  time,  by  the  dew  which 
forms  upon  its  surface,  and  at  length  trickles  down  the  sides 
in  large  drops. 

When  a  portion  of  air  near  the  surface  charged  with  moisture 
is  suddenly  cooled,  the  water  it  contains  is  condensed,  and  be- 
comes visible,  producing  fog  and  mist.  When  the  condensation 
takes  place  in  the  upper  regions  of  the  atmosphere,  it  forms 
clouds.  These  often  remain  freely  suspended  in  the  air  without 
apparent  change,  but  if  a  rise  of  temperature  occurs,  they  gra- 
dually disappear,  the  particles  being  again  dissolved  in  the  air. 
When,  on  the  other  hand,  the  condensation  is  continued  to  a 
certain  point,  the  drops  of  water  fall  to  the  ground,  constituting 
rain.  If  the  cold  is  sufficient  to  freeze  water  in  that  part  of  the 
atmosphere  where  the  condensation  is  taking  place,  snow  is 
produced,  and  falls  in  feather-like  crystals. 

In  that  part  of  the  United  States  on  the  coast  of  the  Atlantic 
Ocean,  it  is  well  known  that  the  snow-storms  usually  come 
from  the  south-west,  commencing  earlier  at  Philadelphia  than 
at  New  York,  and  earlier  at  this  place  than  at  Boston,  &c. ; 
though  the  wind  all  the  time  is  at  the  north-east.  It  is  evident, 
therefore,  that  in  the  upper  regions  of  the  atmosphere,  there  is 
a  current  of  warm  air,  moving  from  the  south-west  to  the 
north-east,  whilst  at  the  surface  a  current  of  cold  air  from  the 
north-east  is  moving  in  the  opposite  direction.  Now,  supposing 
the  warm  air  from  the  south  to  be  highly  charged  with  mois- 
ture, as  it  no  doubt  in  such  cases  is,  we  have  all  the  conditions 

western  part  of  the  Atlantic  ocean?  In  what  direction  do  they  then  pro- 
gress ?  In  what  direction  is  the  whirl  north  of  the  equator  ?  South  of  the 
equator  ?  290.  What  is  always  contained  in  the  atmosphere  ?  What  are 
formed  from  this  vapour  ?  From  what  is  this  vapour  formed  ?  During  what 
season  is  it  produced  most  rapidly  ?  How  may  the  presence  of  this  vapour 
be  shown  in  warm  weather  ?  How  is  fog  produced  ?  What  is  mist  ?  How 
are  clouds  formed  ?  What  may  often  occasion  the  disappearance  of  clouds 
that  have  remained  a  time  suspended  in  the  air?  How  is  rain  produced? 
How  is  snow  produced  ?  In  what  part  of  the  United  States  bordering  on  the 
Atlantic  ocean  is  it  observed  that  snow-storms  usually  first  commence  ?  In 
what  direction  does  the  wind  usually  blow  during  these  storms  ?  What  must 
be  the  direction  of  the  wind  in  the  higher  parts  ofthe  atmosphere  ?  How  will 


L 


PNEUMATICS.  153 

necessary  for  the  production  of  snow.  The  moisture  of  the 
warm  air,  in  mixing  with  colder  current  from  the  north,  is  not 
only  condensed  but  frozen,  and  falls  to  the  earth  as  snow,  in 
accordance  with  our  principles. 

291.  Hail  is  produced  by  the  freezing  of  the  drops  after 
they  are  formed,  by  their  passing  through  cold  strata  of  the 
atmosphere,  in  the  course  of  their  descent.  In  some  few  in- 
stances which  have  been  recorded,  hail-stones  of  enormous  size 
have  fallen,  even  several  inches  in  diameter,  —  a  fact  which 
seems  to  indicate  that  a  rapid  accumulation  must  have  taken 
place  during  their  descent,  from  the  moisture  contained  in  the 
atmosphere. 

292.  The  rain-gauge  is  an  instrument  for  measuring 
the  quantity  of  water  which  falls  in  the  form  of  rain, 
hail,  &c,  in  a  given  time  in  any  place.  This  quantity 
is  usually  estimated  in  inches ;  and  when  it  is  said  that 
an  inch  of  rain  has  fallen,  the  meaning  is  that  if  the 
surface  of  the  earth  were  perfectly  level,  the  water 
which  has  fallen  at  the  time  supposed  would  be  suffi- 
cient to  cover  it  an  inch  deep. 

There  are  several  varieties  of  the  rain-gauge,  but 
one  of  the  following  construction  answers  the  purpose 
well,  and  is  convenient  to  use.  A  B,  figure  142,  is  a 
glass  tube  an  inch  in  diameter,  and  from  2  to  3  feet 
in  length,  and  has  cemented  upon  it  at  the  top  a  me- 
tallic vessel  or  funnel,  C,  the  mouth  of.  which  is  four 
times  that  of  the  tube  itself;  consequently,  an  inch  of 
water  in  the  funnel  must  fill  the  tube  four  inches.  By 
the  side  of  the  tube  a  scale  is  attached  graduated  into 
inches  and  proportional  parts,  which,  however,  are 
made  four  times  as  long  as  the  common  inch.  Now, 
as  the  mouth  of  the  funnel  is  four  times  that  of  the 
tube,  an  inch  of  rain  falling  into  the  funnel  will  fill  the 
tube  four  inches,  or  just  one  of  our  divisions. 

To  determine  the  quantity  of  rain  which  falls,  the 
instrument  is  to  be  attached  to  an  upright  post,  and 
placed  at  a  distance  from  any  building, ~so  that  even 
Fi    M2    in  windy  weather  the  rain  shall  fall  freely  into  it. 
Snow  and  hail  are  to  be  caught  in  a  vessel,  the  mouth 
of  which  is  of  the  same  size  as  that  of  the  rain-gauge;  and  after 
it  is  melted,  the  quantity  of  water  is  to  be  determined  by  pour- 
ing it  into  the  gauge. 

the  mingling  of  two  such  currents  produce  the  results  which  are  witnessed  ? 
291.  How  is  hail  formed  ?  Do  the  hail-stones  probably  increase  during  their 
fall  ?  292.  What  is  the  design  of  the  rain-gauge  ?  What  is  meant  when  it 
is  said  an  inch  of  rain  has  fallen  ?  How  is  the  rain-gauge,  represented  in 
figure  142,  constructed  ?  How  much  larger  is  the  mouth  of  the  tube  than 
the  tube  itself  ?  How  high  does  an  inch  of  rain  fill  the  tube  ?  Will  the  quan- 
tity of  rain  that  falls  in  windy  weather  be  accurately  indicated  ? 


154 


NATURAL     PHILOSOPHY. 


CHAPTER  IV. 


ACOUSTICS. 


293.  ACOUSTICS  is  the  science  of  sound,  and  has  for  its  appro- 
priate object  everything  which  affects  the  organs  of  hearing. 

Sound  is  the  result  of  a  vibratory  motion  produced  in  the 
air  or  some  other  elastic  body.  Usually,  whatever  may  be  the 
body  in  wL?ch  this  vibratory  motion  is  first  produced,  it  is  con- 
veyed to  the  ear  by  means  of  the  air. 

294.  When  these  vibrations  take  place  in  a  uniform,  regular 
manner,  a  perfect  sound  or  tone  is  produced ;  but  if  the  vibra- 
tions are  irregular  and  interrupted,  a  mere  noise  results. 

The  vibration  of  a  sounding  body  may  often  be 
seen  by  the  eye,  as  in  the  case  of  the  lower  strings  of 
the  violoncello,  or  the  prongs  of  the  common  tuning- 
fork.  The  form  of  this  last  instrument  is  seen  in 
figure  143.  When  it  is  held  by  the  handle,  and  the 
two  prongs  pressed  together  and  suddenly  released, 
or  one  ofthem  struck  against  some  solid  substance, 
a  distinct  sound  is  heard ;  and  by  close  inspection  the 
prongs  may  be  seen  in  rapid  vibration  to  and  from 
each  other,  as  indicated  by  the  dotted  lines.  The 
particles  of  dust  or  sand  upon  a  bell,  when  it  is  struck, 
are  observed  to  be  put  in  rapid  motion. 

295.  Sound  is  conveyed  from  the  vibrating  body  to 
the  ear  by  means  of  vibrations  in  the  air,  as  already 
stated ;  hence,  if  a  bell  is  placed  under  the  receiver 
of  an  air-pump,  as  the  air  is  exhausted  its  sound  be- 
comes less  and  less  distinct,  until  it  can  scarcely  be 
heard.  If  the  air  be  now  gradually  readmitted,  and 
the  bell  in  the  mean  time  rung,  the  sound  will  be  ob- 
served to  increase  in  intensity  in  proportion  as  the 
density  of  the  air  in  the  receiver  increases. 


Fig.  143. 


Quest.  293.  What  is  the  object  of  the  science  of  acoustics  ?  What  is 
sound  the  result  of?  How  are  sounds  conveyed  to  the  ear  ?  294.  What  is 
the  result  when  the  vibrations  are  regular  ?  and  what  when  they  are  irregu- 
lar and  interrupted  ?  May  the  vibrations  of  the  sounding  body  be  some- 
times seen  by  the  eye  ?  What  is  the  form  of  the  tuning-fork  ?  295.  What 
is  the  effect  if  a  bell  be  struck  several  times  as  the  air  is  exhausted  from 
a  receiver  under  which  it  is  placed  ?  What  will  be  the  effect  as  the  air 
is  again  admitted  ?  How  is  a  bell  made  to  ring  under  an  exhausted  re- 
ceiver ? 


ACOUSTICS. 


155 


- 144- 


Figure  144  represents  an  apparatus 
which  is  used  for  this  purpose.  It  is  so 
constructed  that  by  pulling  the  rod  up- 
ward, which  passes  air-tight  through  the 
neck  of  the  receiver,  the  small  bell  is 
made  to  ring  without  admitting  the  air. 
The  apparatus  must  not  be  allowed  to 
touch  the  receiver,  nor  should  it  stand 
directly  upon  the  plate  of  the  air-pump, 
as  the  vibrations  will  then  be  partially 
communicated  through  the  solids  to  the 
external  air,  and  thence  to  the  ear.  A 
piece  of  sheet  India-rubber  answers  well 
to  insulate  it  from  the  plate  of  the  pump. 
296.  Sounds  are  less  intense  on  high 
mountains  than  in  the  valleys  below,  in 
consequence  of  the  diminished  density 
of  the  atmosphere.  This  would  be  expect- 
ed from  the  experiment  just  described ; 
yet  the  explosions  of  meteors  at  vast 
elevations  have  often  been  heard.  In 
condensed  air  sounds  become  more  intense;  an  increased 
loudness  of  the  voice  is  always  observed  by  persons  descending 
beneath  the  surface  of  the  sea  in  diving-bells  (§  265),  where 
the  density  of  the  air  is  greatly  increased  by  the  pressure  of 
the  water. 

297.  In  comparing  different  sounds,  the  ear  readily  distin- 
guishes three  peculiarities,  viz :  intensity  or  loudness,  pitch,  and 
quality,  called  by  the  French  timbre.  The  difference  of  sounds 
in  intensity  or  loudness  depends  upon  the  greater  or  less  ex- 
tent of  the  vibrations,  and  are  readily  perceived  by  every  one ; 
but  variations  of  pitch  are  not  so  easily  recognised,  at  least  by 
the  uneducated  ear.  In  music,  differences  of  pitch  are  desig- 
nated by  the  terms  high  and  low,  sharp  and  flat,  acute  and 
grave.  But  sounds  precisely  alike  in  intensity  and  pitch  may 
yet  differ  in  a  third  respect,  which,  for  want  of  another  term, 
we  have  called  quality.  Thus,  a  wire  extended  over  a  table 
made  of  pine  wood  will  give  a  different  sound  from  another 
extended  over  an  oak  table,  though  both  are  at  the  same  pitch, 
and  are  alike  as  it  regards  intensity.  So  the  sound  of  a  flute 
and  that  of  a  violin,  when  playing  the  same  tune,  are  entirely 
unlike  as  it  respects  this  peculiarity. 

Quest.  296.  Why  are  sounds  less  intense  on  high  mountains  than  in  deep 
valleys  ?  Have  the  explosions  of  meteors  been  heard  at  great  heights  ? 
How  is  the  intensity  of  sounds  affected  in  diving-bells  as  they  are  made  to 
descend  beneath  the  surface  ?  297.  What  three  peculiarities  in  sound  does 
the  ear  readily  distinguish?  Upon  what  does  intensity  depend  ?  How  are 
differences  of  pitch  designated  in  music  ?  If  two  sounds  are  alike  in  pitch 
and  loudness,  in  what  other  respect  may  they  differ  ?  How  is  this  illustrated  ? 
Can  we  distinguish  different  instruments  when  playing  the  same  tune? 


150  NATURAL     PHILOSOPHY. 

293.  The  intensity  of  sound,  like  that  of  attraction  ($34) 
diminishes  as  the  square  of  the  distance  from  the  sounding 
body  increases.  The  distance  at  which  a  sound  may  be  heard 
depends  very  much  upon  circumstances,  as  the  state  of  the 
weather,  the  direction  and  force  of  the  wind,  nature  of  the  sur- 
face over  which  the  sound  passes,  &c.  The  noise  of  the  cannon 
at  the  battle  of  Bunker  Hill  was  heard  at  Pittsfield  (Mass.)  120 
miles  distant,  over  the  uneven  surface  of  the  land ;  but  over 
the  level  surface  of  the  sea  the  firing  of  guns  has  been  heard 
at  the  distance  of  200  miles.  In  one  instance  two  persons  held 
a  conversation  together  over  a  frozen  harbour  a  mile  and  a 
quarter  wide.  So  it  is  observed  that  sounds  are  heard  along 
a  smooth  wall  much  farther  than  in  open  space.  On  the  same 
principle,  tubes,  by  confining  sound  and  preventing  it  from 
spreading,  may  be  made  to  conduct  it  a  great  distance.  In 
large  manufactories  speaking-tubes  are  often  used,  which,  ex- 
tending from  the  overseer's  room  to  distant  parts  of  the  build- 
ing, enable  him  to  give  his  directions  with  precision,  and  with- 
out delay. 

299.  Pitch  depends  upon  the  number  of  vibrations  made  by 
the  sounding  body  in  a  given  time.  The  lowest  sound  that  can 
be  heard  is  produced  by  about  32  vibrations  a  second,  and  the 
highest  by  not  more  than  10  or  12  thousand;  though  it  is  found 
that  ears  differ,  some  being  capable  of  hearing  sounds  so 
sharp  as  to  be  entirely  inaudible  to  others.     If  the  number  of 
vibrations  is  less  than  about  32  per  second,  the  ear  distin- 
guishes them  separately,  and  a  succession  of  blows  is  heard, 
the  idea  of  a  continuous  sound  not  being  produced.     This 
is  shown  by  making  the  end  of  a  spring  play  against  a  toothed 
wheel.     When   the  wheel   is  turned   slowly,   the  successive 
blows  of  the  spring  are  heard,  and  may  even  be  counted ;  but 
if  the  velocity  is  sufficiently  increased,  the  blows  are  made  to 
succeed  each  other  so  rapidly  that  the  ear  is  incapable  of  se- 
parating them,  and  a  continuous  sound  is  produced.     As  the 
wheel  is  made  to  turn  more  and  more  rapidly,  the  pitch  be- 
comes sharper  and  sharper,  until  the  ear  is  incapable  of  judg- 
ing concerning  it. 

300.  Sound  moves  from  place  to  place  through  the  air  with 
a  velocity  of  about  1125  feet  per  second,  or  12|  miles  a  minute, 
and  765  miles  an  hour.    It  is  found,  however,  that  this  velocity 
is  somewhat  affected  by  the  temperature,  state  of  the  weather, 
winds,  &c.  By  knowing  the  time  that  elapses  after  the  produc- 

Quest.  298.  How  does  the  intensity  of  sounds  diminish  with  the  distance  ? 
How  far  may  sounds  be  heard  ?  Why  may  sounds  be  heard  further  along  a 
smooth  wall  or  over  a  smooth  surface  than  in  other  situations  ?  For  what 
purpose  are  speaking-tubes  used  ?  299.  Upon  what  does  pitch  depend  ? 
How  many  vibrations  are  required  in  a  second  to  produce  the  lowest  sound 
audible  to  the  ear  ?  How  many  to  produce  the  highest  sound  ?  How  is  this 
illustrated  by  the  toothed  wheel  and  spring  ?  300.  With  what  velocity  doea 
sound  move  ?  Is  this  velocity  varied  by  circumstances  ?  How  may  we  de- 


ACOUSTICS.  157 

tion  of  a  sound,  we  may  therefore  readily  determine  the  dis- 
tance of  its  origin,  with  some  degree  of  accuracy.  Thus, 
suppose  that  after  seeing  the  flash  of  a  cannon  fired  at  a  dis 
tance,  30  seconds  elapse  before  the  report  is  heard;  as  the 
sound  must  have  advanced  1125  feet  every  second,  the  whole 
distance  to  the  place  where  the  cannon  was  fired  must  be  30 
times  1125,  or  33,750  feet,  equal  to  about  6}  miles. 

Suppose,  again,  that  in  a  thunder-storm,  a  flash  of  lightning 
is  seen  10  seconds  before  the  thunder  is  heard;  at  what  dis- 
tance did  the  explosion  take  place!  Evidently  it  must  have 
been  10  times  1125,  or  11,250  feet,  or  about  2j[-  miles. 

301.  Sound  is  conveyed  in  liquids  and  solids  with  greater 
velocity  than  in  air.    In  water,  sound  moves  with  a  velocity  of 
about  4708  feet  per  second,  being  more  than  4  times  its  velocity 
in  the  air.     A  bell  struck  under  water  in  the  lake  of  Geneva 
was  heard  at  the  distance  of  9  miles,  the  sound  having  been 
conveyed  by  the  water. 

Solids  conduct  sound  with  still  greater  velocity  than  liquids. 
It  has  been  determined  by  experiment  that  cast-iron  will  con- 
vey sound  about  11,090  feet  per  second,  or  about  10  times  its 
velocity  in  air ;  while  in  some  other  metals,  and  some  kinds  of 
wood,  it  travels  with  still  greater  speed. 

Some  very  easy  experiments  serve  to  show  the  power  of 
solids  to  conduct  sound.  If  a  person  places  his  watch  on  one 
end  of  a  long  stick  of  timber,  and  going  to  the  other  end, 
presses  his  ear  against  it,  he  will  hear  its  ticking  almost  as 
distinctly  as  if  his  ear  were  directly  against  the  watch.  If  his 
watch  is  placed  on  a  table,  and  he  touches  it  with  one  end  of  a 
long  slender  pole,  bringing  the  other  end  to  his  ear,  the  ticking 
will  be  distinctly  heard.  If  any  part  of  a  continuous  brick  wall 
be  struck  with  a  hammer,  the  sound  will  usually  be  heard  by  a 
person  placing  his  ear  against  it  in  any  other  part  of  the  build- 
ing, however  distant.  The  experiment  is  best  performed  on 
walls  dividing  the  interior  of  buildings  in  which  there  are  but 
few  openings  for  doors  or  windows. 

302.  Sounds  pass  with  difficulty  from  one  medium  to  another, 
as  from  air  to  a  solid  and  from  the  solid  to  the  air  again. 
Hence,  a  voice  in  a  room,  if  not  very  loud,  is  heard  but  indis- 
tinctly in  another  separated  from  it  by  a  continuous  wall; 
since,  being  made  in  the  air,  it  has  to  be  transmitted  to  the 
solid  constituting  the  partition,  and  then  again  to  the  air.     If  a 
light  blow  is  struck  on  the  dividing  wall  in  one  room,  it  is  dis- 
tinctly heard  by  a  person  standing  against  the  wall  in  the 

temiine  the  distance  at  which  a  cannon  is  fired,  or  the  distance  of  a  thunder- 
cloud ?  301.  Do  liquids  and  solids  convey  sounds  more  rapidly  than  air  ? 
What  is  the  velocity  with  which  sound  passes  in  cast-iron  ?  What  experi- 
ments are  given  to  prove  that  solids  convey  sound  ?  302.  What  is  said  of 
the  passage  pf  sound  from  one  medium  to  another  ? 


158  NATURAL     PHILOSOPHY. 

other,  because  it  is  conducted  directly  through  by  the  solid 
material  of  the  wall. 

303.  Sound  is  readily  reflected  from  smooth  surfaces,  making 
the  angles  of  incidence  and  reflection  equal,  like  the  elastic 
ball  when  striking  obliquely  against  a  smooth  surface.     This 
constitutes  what  is  called  an  echo.    A  wall,  the  side  of  a  house, 
the  surface  of  a  rock,  the  ceiling  and  walls  of  an  apartment, 
give  rise  to  echoes  which  are  more  or  less  audible.  When  there 
are  several  surfaces  at  different  distances  from  the  place  where 
the  sound  is  produced,  the  echo  will  often  be  repeated  from 
each  surface  in  succession.     At  a  place  in  Oxfordshire,  Eng- 
land, a  single  syllable  is  thus  repeated  no  less  than  17  times. 
In  such  a  place,  a  single  ha,  distinctly  pronounced,  is  returned 
in  a  ha  ha  ha — a  hearty  laugh  ! 

In  a  cathedral  in  Sicily,  the  slightest  whisper  behind  the  high 
altar  may  be  heard  at  the  opposite  extremity  of  the  building,  a 
distance  of  250  feet. . 

When  the  echoing  surface  is  concave  towards  the  person 
listening,  the  sound  reflected  from  it  will  converge  to  a  point, 
and  will  often  be  greatly  increased  in  intensity.  This  is  often 
observed  in  churches  and  public  halls  with  vaulted  roofs,  in 
which  there  is  usually  a  certain  place,  depending  upon  the 
position  of  the  speaker,  where  he  can  be  heard  more  distinctly 
than  in  any  other  part.  In  a  church  with  which  the  writer  is 
acquainted  in  the  state  of  Maine,  having  the  pulpit  at  one  ex- 
tremity, there  is  no  better  place  to  hear  the  sermon  than  at  the 
foot  of  the  gallery  stairs  at  the  other  extremity,  entirely  out  of 
sight  both  of  the  preacher  and  his  audience.  As  the  church  is 
not  large,  the  preacher  is  heard  without  difficulty  in  all  parts 
of  it ;  but  the  peculiar  distinctness  with  which  every  word  is 
heard  at  the  point  alluded  to,  is  no  doubt  occasioned  by  the 
reflection  of  the  sound  from  the  ceiling  or  roof  above. 

In  case  either  of  the  walls  or  roof  of  a  church  or  hall  design- 
ed for  public  speaking  is  made  concave,  as  has  sometimes  been 
recommended,  there  must  always  be  some  favoured  part  where 
the  speaker  will  be  heard  better  than  in  other  parts ;  hence, 
when  it  is  designed  that  all  the  audience  shall  fare  alike  in  this 
respect,  the  best  form  that  can  be  given  to  them  is  to  have 
them  perfectly  plain. 

304.  The  rolling  sound  of  thunder,  and  its  sudden  bursts 
and  variations  of  intensity,  are  occasioned,  it  is  supposed, 

Quest.  303.  May  sounds  be  reflected  ?  What  is  an  echo  ?  What  objects 
will  yield  an  echo  ?  When  there  are  several  echoing  surfaces  at  different 
distances,  what  is  the  effect  ?  At  what  distance  is  it  sa.id  a  whisper  will  be 
echoed,  so  as  to  be  audible,  in  a  certain  cathedral  in  Sicily  ?  What  is  the 
effect  when  the  echoing  surface  is  concave  ?  What  will  be  the  effect  of 
making  the  roof  or  walls  concave  of  a  large  room  designed  for  public  speak- 
ing ?  What  is  the  best  form  for  the  walls  and  roof  of  a  room  designed  for 
this  purpose  ?  304.  How  is  it  supposed  the  rolling  sound  of  thunder  is  pro- 


ACOUSTICS.  159 

chiefly  by  numerous  echoes  from  separate  masses  of  clouds 
floating  in  the  air  at  different  distances,  which  will  of  course 
arrive  at  the  ear  successively.  It  may  be  also  that  the  electric 
spark  darting  through  the  air  produces  the  sound,  not  in  a 
single  point,  but  all  along  its  zigzag  course,  at  different  dis- 
tances from  the  ear.  The  original  report,  therefore,  though 
perfectly  instantaneous,  yet  being  produced  at  different  dis- 
tances from  the  ear,  will  arrive  from  different  points  in  suc- 
cessive parts,  and  will  thus  become  prolonged. 

The  production  of  echoes  often  depends  upon  the  state  of 
the  atmosphere  as  it  regards  barometric  pressure,  temperature, 
moisture,  the  direction  and  force  of  the  wind,  &c.  Thus,  we 
can  occasionally  hear  a  very  distinct  echo  from  a  distant 
building,  or  other  object,  from  which  an  audible  return-sound 
cannot  usually  be  obtained. 

305.  When  a  distinct  echo  can  be  obtained  from  a  distant 
object,  it  may  be  made  use  of  to  determine  its  distance.  Thus, 
suppose  that  from  a  building  on  the  opposite  bank  of  a  river, 
an  echo  is  returned  to  an  observer  in  4  seconds,  it  is  required 
to  determine  the  width  of  the  river.  As  the  sound  must  go  and 
return,  it  is  evident  the  distance  must  be  equal  to  that  over 
which  sound  would  pass  in  half  the  time,  or  2  seconds.     Its 
width  is,  therefore,  1125x2=2250  feet,  or  750  yards. 

306.  Sounds  in  the  open  air  are  partially  intercepted  by 
opposing  obstacles,  forming  what  has  been  called  an  acoustic 
shadow.  Thus,  a  band  of  music,  in  passing  through  the  streets, 
is  heard  much  less  distinctly  after  going  behind  a  block  of 
buildings,  than  before  any  object  intervened.    In  water,  sounds 
are  almost  entirely  cut  off  by  intervening  objects. 

307.  We  have  seen 
above  (§  298),  that  tubes 
may  be  made  to  convey 
sound  distinctly  a  consi- 
derable distance,  which 
Fis- 145-  no  doubt  is  to  be  attri- 

buted to  the  reflection  of  the  sonorous  waves  from  side  to  side 
in  their  passage.  ,It  is  on  this  principle  too  that  the  speaking- 
trumpet  acts,  by  which  a  person  is  enabled  to  hold  a  conversa- 
tion with  another  at  a  much  greater  distance  than  he  otherwise 
could.  It  is  made  in  the  form  of  a  hollow  cone,  having  a  portion 
removed  at  the  apex  to  which  the  mouth  is  applied,  the  instru- 

duced  ?  May  the  sound  also  be  produced  along  a  line  for  some  distance,  so 
as  to  be  at  different  distances  from  the  ear  ?  Will  the  production  of  an  echo 
from  an  object  often  depend  upon  the  state  of  the  atmosphere  ?  305.  How 
may  we  by  means  of  the  echo  from  a  distant  object  determine  its  distance  ? 

306.  Is  the  passage  of  sound  in  the  open  air  interrupted  by  intervening  ob- 
jects ?  How  is  this  shown  by  a  band  of  music  marching  through  the  streets  ? 

307.  To  what  is  the  conveyance  of  sound  in  tubes  to  be  attributed  ?     On 
what  principle  does  the  speaking-trumpet  act  ?    What  is  its  form  ?    What  is 
the  design  of  the  ear-trumpet  ? 


160  NATURAL     PHILOSOPHY. 

ment  being  directed  towards  the  person  addressed.    It  is  repre- 
sented in  figure  145. 

The  ear-trumpet  is  designed  to  assist  the  hearing  of  persons 
who  are  partialJy  deaf,  by  collecting  the  vibrations  and  con- 
ducting them  to  the  ear.  It  is  made  of  the  same  form  as  the 
speaking-trumpet,  and  is  used  by  applying  the  small  extremity 
to  the  ear. 

308.  Music.  —  Music  is  the  art  of  producing  and  combining 
sounds  in  a  manner  agreeable  to  the  ear.     A  musical  sound  is 
produced  when  the  impulses  or  vibrations  occur  at  exactly 
equal  intervals,  and  are  of  similar  intensity  and  quality.    Such 
a  sound  always  produces  a  pleasing  effect  upon  the  mind;  but 
if  too  long  continued,  it  becomes  tedious  and  requires  to  be 
changed. 

309.  Though  intensity  and  quality  are  by  no  means  to  be 
neglected  in  music,  yet  the  most  important  circumstance  to  be 
attended  to  is  pitch.     This  we  have  seen  (§  299)  depends  en- 
tirely upon  the  frequency  of  the  vibrations,  or  the  number 
which  occur  in  a  given  time ;  and  two  sounds  in  which  these 
elementary  impulses  occur  with  the  same  frequency  are  said 
to  be  in  unison  or  to  have  the  same  pitch,  whatever  may  be 
their  intensity  or  quality. 

______  310.  A  stretched  cord  or  wire  fur- 

nishes an  excellent  instrument  for  the 

****i_?^==    T^^r^ff-^    investigation  of  many  points  connect- 
ed with  this  subject.     When  such  a 
Fig.  146.  cord  or  wire  is  drawn  a  little  out  of 

its  position  of  rest,  and  suddenly  let  go,  it  will  continue  for  a 
time  to  vibrate  backward  and  forward  over  its  position  of  rest, 
as  represented  in  figure  146,  producing  a  sound  gradually  dimi- 
nishing in  intensity,  but  continuing  of  the  same  pitch  until  it 
ceases.  The  vibrations  of  a  cord  are  much  better  excited  by  a 
bow,  which,  as  is  well  known,  consists  of  a  bundle  of  horse- 
hairs loosely  stretched  by  means  of  an  instrument  for  the  pur- 
pose, and  rubbed  with  rosin  to  make  them  adhesive.  The  pitch 
of  such  a  cord  or  wire  is  found  to  depend  upon  three  circum- 
stances, viz :  its  length,  size  or  weight,  and  the  force  with  which 
it  is  stretched.  By  an  increase  of  the  length  or  of  the  weight, 
the  pitch  is  made  to  fall,  or  become  more  grave ;  but  by  in- 
creasing the  tension,  it  becomes  more  acute  or  sharp. 
Hence,  the  same  cord  may  be  made  to  give  sounds  of  different 

Quest.  308.  What  is  music  1  How  is  a  musical  sound  produced  1  Are 
the  intensity  and  quality  of  musical  sounds  important  1  309.  What  is  the 
most  important  circumstance  requiring  attention  1  Upon  what  does  the  pitch 
depend  1  When  are  two  sounds  said  to  be  in  unison  1  310.  How  is  a  stretch- 
ed cord  made  to  vibrate  so  as  to  produce  a  sound  1  For  what  purpose  is 
the  bow  used  with  a  stringed  instrument,  as  the  violin  1  Upon  what  will  the 
pitch  of  such  a  cord  depend  1  By  what  change  may  the  same  cord  be 
made  to  give  sounds  of  different  pitch  1  How  is  this  accomplished  in  the 
violin  and  violoncello  1 


ACOUSTICS.  161 

pitch  by  simply  changing  its  length.  This  is  done  in  stringed 
instruments  like  the  violin  and  violoncello,  by  pressing  the 
string  upon  a  support  placed  just  below  it,  while  the  bow  is 
drawn  over  it.  In  the  piano  forte,  each  wire  gives  but  a  single 
sound  to  which  it  is  adjusted,  depending  upon  the  three  cir- 
cumstances above  named. 

311.  Sometimes  a  string  does  not  vibrate  as  a  whole,  but 
divides  itself  spontaneously  into  parts,  each  of  which  vibrates 
separately,  producing  its  own  note,  which  is  the  same  as  if  the 
string  was  only  of  that  length.  The  points  of  division  between 
the  parts  vibrating  in  such  a  case,  are  called  nodes,  or  nodal 
points. 

312.  In  wind  instruments,  as  the  organ,  flute,  &c.,  the  vibra- 
tions are  produced  in  the  column  of  air  within  the  instrument, 
and  depend  upon  its  length,  and  in  some  respects  also  upon 
the  size.    In  the  organ,  the  different  sounds  are  produced  by 
different  pipes,  each  of  which  is  so  adjusted  as  to  produce  a 
single  sound  of  the  proper  pitch ;  but  in  the  flute,  clarinet, 
&c.,  different  lengths  are  given  to  the  vibrating  column  by  the 
fingers  and  keys  opening  and  stopping  the  apertures,  as  may 
be  required.    The  note  produced  by  one  of  these  instruments 
will  also  depend  to  some  extent  upon  the  manner  of  blowing  it. 

Wind  instruments  are  of  two  kinds,  those  with  reeds,  and 
those  without  them.  Of  the  former  kind  are  the  clarinet  and 
bassoon ;  of  the  latter,  the  flute,  serpent,  bugle,  &c.  In  the 
accordion,  the  sound  is  produced  entirely  by  reeds,  which  are 
slender  strips  of  metal  made  to  vibrate  in  a  small  aperture, 
through  which  the  air  passes. 

313.  Music  may  be  considered  as  composed  of  two  parts, 
melody  and  harmony.    Melody  depends  upon  the  order  or  suc- 
cession of  the  sounds,  and  the  time  during  which  they  are 
severally  continued.    A  musical  sound,  however  pleasing  at 
first,  soon  becomes  disagreeable  if  continued,  and  must  there- 
fore be  succeeded  by  another,  and  this  by  a  third,  and  so  on. 
Now  the  peculiar  order  in  which  the  several  sounds  succeed 
each  other  in  a  piece  of  music,  constitutes  its  melody.    Har- 
mony, on  the  other  hand,  depends  upon  the  union  or  blending 
of  two  or  more  different  sounds,  which  must  sustain  certain 
relations  of  pitch  to  each  other.  When  two  sounds  heard  toge- 
ther produce  an  agreeable  effect  upon  the  ear^  they  are  said  to 
chord,  or  to  form  a  chord ;  when  they  do  not  harmonize  so  as 

Quest.  311.  May  a  string  sometimes  vibrate  in  parts  ?  What  are  the  nodes 
or  nodal  points  ?  312.  In  wind  instruments,  what  is  to  be  considered  the 
vibrating  body  ?  Upon  what  will  the  pitch  depend  ?  How  are  the  different 
sounds  produced  in  the  organ  ?  How  in  the  flute,  clarinet,  &c.  ?  Will 
the  manner  of  blowing  the  flute  also  affect  the  note  it  will  give  ?  313.  What 
two  parts  may  music  be  considered  as  composed  of?  Upon  what  does  me- 
lody depend  ?  Will  a  musical  sound  that  is  at  first  pleasing  become  disagree- 
able if  long  continued  ?  Upon  what  does  harmony  depend  ?  When  are  two 
sounds  said  to  chord  ?  When  are  two  sounds  said  to  produce  a  discord  ? 
14* 


9 

162  NATURAL     PHILOSOPHY. 

to  produce  this  agreeable  effect,  they  are  said  to  be  discordant, 
or  to  produce  a  discord. 

314.  The  first  and  best  chord  is  called  a  unison.    It  is  produced  by  two 
sounds  having  the  same  pitch ;  that  is,  two  sounds  whose  vibrations  are 
performed  in  the  same  time.     The  next  chord  or  concord  is  the  octave,  in 
which  the  vibrations  are  as  1  to  2.     As  third  in  point  of  agreeableness, 
we  may  mention  the  twelfth  from  the  fundamental  note,  in  which  the 
vibrations  are  as  1  to  3 ;  and  next,  the  fifth,  in  which  the  vibrations  are 
as  2  to  3. 

315.  If  we  begin  with  any  particular  sound,  and  then  ascend 
by  seven  regular  steps,  we  produce  the  diatonic  or  natural 
scale;  which  is  a  series  of  notes,  that,  with  little  variation, 
has    been    adopted  by  all  nations,  in  all  ages  of  the  world,  as 
the  foundation  of  their  music.     This  scale  is  sometimes  called 
the  gamut.  The  last  or  eighth  note  is  always  the  octave  of  the 
first,  called  the  fundamental  note,  and  seems  to  the  ear  to  be 
merely  a  repetition  of  it.     If  we  ascend  above  this,  or  descend 
below  it  seven  more  notes,  we  only  repeat  the  same  series,  the 
latter  notes  being  the  several  octaves  of  the  former. 

316.  Music  is 
written  on  several 
horizontal  lines  and 
the  intermediate 
spaces,  as  repre- 
sented in  fig.  147; 
and  the  several 
notes  of  the  natural 
scale  are  represent- 
ed by  the  first  se- 
ven letters  of  the 

alphabet,  which  are  placed  as  in  the  figure.  These  notes  are 
also  represented  by  the  seven  syllables  do,  re,  mi,  fa,  sol,  la,  si, 
the  first  syllable  here  used  being  always  applied  to  the  funda- 
mental note,  called  the  tonic,  which  in  the  natural  key  is  always 
on  the  line  or  space  denoted  by  the  letter  C. 

These  several  notes  are  supposed  to  differ  from  each  other 
only  in  pitch,  which,  as  we  have  seen,  depends  entirely  upon 
the  number  of  vibrations  in  a  given  time.  In  producing  these 
sounds,  however,  nothing  depends  upon  the  absolute  number 
of  vibrations,  but  only  their  ratio  to  each  other.  Whatever 
may  be  the  number  of  vibrations  in  the  fundamental  note,  in 
the  second,  or  next  above  it,  there  must  be  9  in  the  same  time 

Quest.  314.  What  is  the  most  agreeable  chord  ?  How  is  it  produced  ? 
What  is  the  next  best  chord  ?  What  the  third  ?  315.  What  is  meant  by 
the  diatonic  or  natural  scale?  What  is  the  eighth  note  considered  ?  316. 
Hew  is  music  written  ?  For  what  are  the  first  seven  letters  of  the  alphabet 
used?  What  syllables  are  used  for  the  same  purpose  ?  In  producing  the 
sounds  of  the  diatonic  scale,  is  the  absolute  number  of  vibrations  in  a  given 
time  to  be  noticed,  or  only  their  ratio  to  each  other  ?  Whatever  may  be  the 
number  of  vibrations  in  a  given  time  in  the  fundamental  note,  how  many 
must  be  made  in  the  same  time  to  produce  the  second,  or  next  above  it  ?  To 


ACOUSTICS. 


163 


in  which  there  are  8  in  the  first.  In  the  third  there  must  be  5, 
while  there  are  4  in  the  first ;  in  the  fourth,  4,  while  there  are  3 
in  the  first,  &c.,  as  will  be  seen  by  the  following  table. 

In  the  following  table,  the  numerator  of  each  fraction  in  the 
second  horizontal  line  indicates  the  number  of  vibrations  made 
in  sounding  the  letter  under  which  it  is  placed,  in  the  same  time 
that  in  sounding  the  fundamental  note,  C,  the  number  of  vibra- 
tions is  made  which  is  expressed  by  the  denominator.  Thus, 
in  sounding  D,  9  vibrations  are  made  in  the  same  time  that  8 
are  made  in  sounding  C ;  in  sounding  A,  5  vibrations  are  made 
in  the  same  time  that  3  are  made  in  sounding  C,  &c. 

In  the  lower  line  are  the  syllables  generally  used  in  singing 
these  several  sounds. 


Letters  

C 

D 

E 

F 

G 

A 

R 

C 

Ratio  of  vibrations 

1 

0 

^ 

1 

} 

3 
2 

1 

V 

2 

Syllables  

Do 

re 

mi 

fa 

sol 

fa 

si 

do. 

\ 

317.  The  space  between  two  notes  is  called  aninterval;  that 
from  any  note  to  the  next,  as  from  the  first  to  the  second,  or 
from  the  second  to  the  third,  is  called  the  interval  of  the  second ; 
that  from  the  first  to  the  third  is  called  the  interval  of  the  third, 
and  so  on.    The  five  intervals  from  C  to  D,  from  D  to  E,  from 
F  to  G,  from  G  to  A,  and  from  A  to  B,  are  very  nearly  equal, 
and  are  called  tones;  while  the  two  from  E  to  F,  and  from  B  to 
C,  are  much  less  than  the  former,  and  are  therefore  called 
semi-tones.    The  whole  octave,  therefore,  contains  five  tones 
and  two  semi-tones.    The  expert  arithmetician  will  perceive 
more  clearly  the  relations  of  the  tones  and  semi-tones  by  re- 
ducing to  a  common  denominator  the  fractions  in  the  second 
horizontal  line  in  the  table,  and  then  comparing  them  together. 

318.  When  all  these  notes  are  sounded  in  succession,  in 
either  the  ascending  or  descending  order,  the  effect  is  always 
pleasing ;  but  the  great  variety  of  melody  in  music  is  produced 
by  causing  these  and  other  intervals  to  succeed  each  other  in 
every  possible  order  and  mode  of  transposition. 

319.  As  has  before  been  stated  ($  313),  when  two  notes  of 
the  scale  are  sounded  together,  a  pleasing  effect  is  produced 
upon  the  ear,  and  it  is  called  a  chord;  or  a  displeasing  effect, 
and  it  is  then  called  a  discord.     But  of  the  chords,  some  are 

produce  the  third,  how  many  must  there  be,  while  there  are  4  in  the  first  ? 
What  is  shown  by  the  upper  and  lower  figures  in  the  second  horizontal 
line  in  the  table  ?  317.  What  is  an  interval?  What  is  the  interval  of  the 
second  ?  What  the  third,  fourth,  &c.  ?  What  are  tones  ?  What  are  semi- 
tones ?  How  many  tones  and  semi-tones  constitute  the  octave  ?  318.  What 
is  the  effect  when  the  notes  of  this  scale  are  sounded  in  succession  ?  How 
is  the  great  variety  produced  in  music?  319.  What  is  the  difference  in  the 


64  NATURAL    PHILOSOPHY. 

iiore  and  some  less  pleasing;  and  so  of  the  discords,  some  are 
much  more  offensive  than  others.  When  two  notes  immediately 
together,  as  C  and  D,  or  D  and  E,  are  sounded  at  the  same 
time,  a  discord  is  always  produced,  which  is  called  the  discord 
of  the  second ;  so  also  C  and  B,  sounded  together,  produce  a 
discord,  called  the  discord  of  the  seventh. 

On  the  other  hand.  C  and  E,  sounded  together,  produce  a 
very  agreeable  chord,  as  do  also  C  and  G.  Numerous  other 
chords  and  discords  may  be  found  by  searching  for  other  com- 
binations, but  we  cannot  here  introduce  them. 

320.  But  what  occasions  the  difference  between  the  chords 
and  discords!  Why  are  the  former  agreeable  and  the  latter 
disagreeable  1 

The  difference  without  question  is  to  be  attributed  to  the 
comparative  rapidity  of  the  vibrations  in  the  two  notes  which 
are  sounded  together.  When  the  vibrations  are  to  each  other 
in  the  simple  ratios  of  1  to  2,  1  to  3,  1  to  4,  2  to  3,  &c.,  it  is  in- 
variably found  that  chords  are  produced,  which  are  more 
agreeable  to  the  ear  as  the  terms  of  the  proportion  are  lower. 

On  the  other  hand,  discordant  notes  are  those  in  which  the 
vibrations  bear  no  simple  ratio  to  each  other.  Thus,  in  the 
discord  of  the  second,  the  vibrations  are  as  8  to  9,  and  in  the 
discord  of  the  seventh,  as  8  to  15. 

This  subject  may  be  illustrated  by  using  waved  lines  to  re- 
present the  different  sounds,  as  in  figures  148,  149,  and  150. 
When  the  interval  between  two  sounds  is  just  an  octave,  the 
number  of  vibrations  in  the  lower  are  to  those  in  the  higher 
sound,  as  1  to  2  ($  314) ;  so  that  every  second  wave  or  vibra- 
tion of  the  latter  sound  will  coincide  with  each  wave  of  the 
former. 

This  is  the  most  simple  ratio  we 
can  have,  and,  as  we  have  seen,  pro- 
duces the  most  agreeable  chord.  The 
sounds  are  illustrated  by  the  waved 
Fig.  H8.  lines  in  figure  148.  The  perpendicular 

lines  show  the  waves  which  coincide. 

When  the  interval  between  two 
sounds  is  what  is  called  a  fifth,  a  very  3 
pleasing  chord  is  produced ;  and  the  2-1 
number  of  vibrations  in  each  in  a 
given  time  are  as  2  to  3,  as  repre-    * 
sented  in  figure  149.    The  perpendicular  lines  indicate,  as  be- 

effect  upon  the  ear  between  a  chord  and  a  discord  ?  Are  all  the  chords 
equally  pleasing  ?  Are  all  the  discords  equally  disagreeable  ?  What  is 
meant  by  the  discord  of  the  second  or  of  the  seventh  ?  320.  To  what  is  the 
difference  between  chords  and  discords  to  be  attributed  ?  When  are  chords 
produced  ?  When  are  the  notes  discordant  ?  How  may  this  subject  be 
illustrated  ?  When  two  sounds  differ  from  each  other  by  an  octave,  what 
vibrations  of  each  will  coincide  ?  When  they  differ  by  a  fifth,  what  vibra- 


ACOUSTICS.  165 

fore,  the  coinciding  waves ;  every  third  one  of  the  sharper 
sound,  it  will  be  seen,  coincides  with  every  other  one  in  the 
lower. 

.      Figure  150  is  designed  to  in- 

9  NAAAA/W\AAAAAAAAA/V|  dicate  what  is  supposed  to  take 
LAAAAAAA!AAAAAAA]  place  in  the  discord  called  the 

8[wwwv\f^^^^Vv^  giscord  of  the  second  (5319)f 

Fig.  i5o.  in  which  the  vibrations  are  as  8 

to  9.    The  coinciding  waves,  it 

will  be  observed,  are  much  farther  from  each  other  than  in  the 
case  of  the  chords  represented  above,  every  9th  of  the  upper 
coinciding  with  the  8th  of  the  lower.  Indeed,  it  is  found  in  the 
case  of  chords,  that,  as  the  coinciding  waves  are  removed  far- 
ther and  farther  from  each  other,  they  become  less  and  less 
pleasing,  and  at  length,  when  removed  to  a  certain  distance, 
decidedly  discordant. 

321.  In  our  description  of  the  diatonic  scale  ($  315),  C  is  taken 
as  the  fundamental  note,  and  the  position  of  the  several  tones 
and  semi-tones  with  reference  to  it  described.    This  is  called 
the  natural  key.    Any  other  letter  may,  however,  be  taken  for 
the  fundamental  note,  but  the  several  tones  and  semi-tones 
must  always  have  their  proper  position  in  relation  to  it.    To 
accomplish  this,  other  keys  are  formed  by  means  of  flats  and 
sharps,  for  a  description  of  which  the  intelligent  student  is  re- 
ferred to  works  that  treat  at  large  on  this  subject. 

322.  Vibrations  of  Bodies.  —  There   are  many   important 
points  connected  with  the  vibrations  of  bodies,  which  have  not 
yet  been  noticed.    Planes,  as  well  as  chords  and  bells,  may  be 
made  to  vibrate  so  as  to  produce  distinct  musical  notes.     A 
plate  of  glass  or  of  metal  answers  well  for  this  purpose,  and  is 
to  be  used  by  holding  it  firmly  in  a  wire  prepared  for  the  pur- 
pose, and  drawing  the  bow  against  the  edge.     It  is  found  that 
the  note  produced  will  depend  upon  the  manner  in  which  it  is 
held  in  the  wire,  and  the  part  against  which  the  bow  is  drawn, 
the  mode  of  using  the  bow,  &c. 

When  a  plate  of  glass  or  metal  is  thus  made  to  vibrate,  the 
vibrations  are  always  performed  in  segments  which  are  se- 
parated by  nodal  lines.  If  the  plate  be  in  a  horizontal  position, 
and  fine  sand  scattered  upon  it,  the  sand  will  leave  the  parts 
in  which  the  motion  is  greatest,  and  collect  on  the  noda] 
lines. 

tions  coincide  ?  What  is  illustrated  by  figure  150  ?  What  vibrations  coincide 
in  this  case  ?  321.  On  what  letter  is  the  fundamental  note  or  tonic  in  the 
natural  key  ?  How  are  other  keys  formed  ?  322.  May  planes  be  made  to 
vibrate  so  as  to  produce  musical  sounds  ?  How  may  a  plate  of  glass  be  used 
for  this  purpose  ?  Will  the  plate  always  vibrate  in  segments  ?  How  may 
the  nodal  lines  be  shown  ?  Will  these  lines  always  occupy  the  same  posi- 
tion ?  What  is  illustrated  by  figures  151  and  152  ? 


166  NATURAL     PHILOSOPHY. 


If  the  plate  is  of  a  rectangular  form  and 
held  by  the  centre,  when  the  bow  is  drawn 
near  one  of  the  corners,  the  sand  will  arrange 
itself  as  in  figure  151.  If  the  bow  is  then  ap- 

plied  to  the  middle  of  one  of  the  sides,  the 

FJ    isi  figures  first  formed  will  be  at  once  broken  up, 

and  the  sand  will  be  thrown  into  the  position 
represented  in  figure  152.  In  some  instances 
differences  in  the  arrangement  of  the  sand  will 
be  produced  by  different  modes  of  using  the  bow 
as  just  intimated;  and  for  every  arrangement 
of  the  sand  a  distinct  tone  is  always  produced. 
If,  for  instance,  a  circular  plate  is  used,  held  by 
the  centre,  and  the  bow  rubbed  against  it  very 
lightly,  the  circumference  will  be  divided  into  four  parts,  and  a 

low  note  will  be  pro- 
duced, the  sand  ar- 
ranging itself  as  in  A, 
figure  153.  If  the  bow 
is  then  pressed  a  little 
harder  against  the 
edge,  the  sound  will 
become  sharper,  the 
figures  first  formed  by 
the  sand  will  be  broken 

up,  and  a  new  arrangement  take  place  as  in  B,  in  which  the 
circumference  is  divided  into  six  parts  or  segments.  By  proper 
means  the  same  plate  may  be  made  to  give  still  higher  sounds, 
the  sand  each  time  forming  a  distinct  arrangement,  and  show- 
ing that  the  circumference  is  divided  by  the  vibrations  into  a 
still  greater  number  of  parts,  as  8  or  12. 

323.  The  parts  of  a  glass  vessel,  as  a  tumbler,  may  be  easily 
made  to  vibrate  and  give  a  musical  sound  by  drawing  a  violin- 
bow  across  the  edge,  or  by  wetting  the  finger  and  rubbing  it 
on  the  edge.    If  the  vessel  is  partly  filled  with  water,  the  vibra- 
tions of  the  glass  will  give  a  peculiar  tremulous  motion  to  the 
surface.    If  the  vessel  be  large,  it  may  be  made  to  vibrate  so 
rapidly  as  to  throw  it  to  pieces. 

324.  Vibrations  in  one  body  may  be  communicated  from  it 
to  another  through  intermediate  solid  bodies,  or  even  through 
the  air.     The  heads  of  a  small  drum  will  always  be  seen  to 
vibrate  when  a  larger  one  near  it  is  struck,  even  though  they 
do  not  touch  each  other.     The  vibrations  are  communicated 
through  the  air.  So  when  the  note  D  is  sounded  on  the  largest 
string  of  the  violoncello,  the  D  string  above,  if  in  tune,  will  be 

Quest.  323.  How  may  a  tumbler  or  other  glass  vessel  be  made  to  vibrate 
so  as  to  produce  a  musical  sound  ?  Will  there  be  any  danger  of  breaking 
the  vessel  in  performing  the  experiment  ?  324.  May  the  vibrations  of  one 
body  be  communicated  to  another  ?  What  purpose  does  the  body  of  a  violin 


ACOUSTICS.  167 

observed  to  vibrate  rapidly,  the  vibrations  being  transmitted 
cither  through  the  air,  or  through  the  solid  parts  of  the  instru- 
ment. 

The  jarring  of  the  earth  by  heavy  thunder  is  no  doubt  to  be 
explained  on  the  same  principle ;  the  immense  vibrations  are 
communicated  even  to  the  solid  earth. 

T.he  body  of  the  violin,  violoncello,  guitar,  &c.,  is  designed, 
by  vibrating  in  unison  with  the  sounds  of  the  strings,  to  in- 
crease the  intensity.  Without  this  assistance  the  sounds  would 
be  scarcely  audible  at  the  distance  even  of  a  few  feet.  A  music 
box  placed  on  a  table,  while  playing  sounds  much  louder  than 
when  held  in  the  hand  for  the  same  reason. 

Formerly,  "  sounding-boards"  were  placed  over  the  pulpits  in  churches, 
with  the  design  of  assisting  the  voice  of  the  speaker,  but  the  practice  is 
now  discontinued  as  useless. 

325.  The  Ear.  —  The  parts  of  the  ear  are  very  different  in 
different  species  of  animals ;  but  in  all,  and  especially  in  man, 
they  are  exceedingly  complex  and  difficult  to  be  fully  under- 
stood. 

The  external  ear  in  some  animals,  as  the  ox  and  the  horse, 
is  evidently  designed  to  collect  the  vibrations,  like  the  ear- 
trumpet  (§  307),  used  by  the  deaf,  and  convey  them  to  the 
organs  of  hearing  within,  thus  increasing  the  intensity  of  the 
sound.  These  animals,  therefore,  have  the  power  of  turning 
their  ears  in  different  directions  from  which  the  sound  may 
proceed.  The  horse,  if  suddenly  startled,  will  always  be  ob- 
served to  turn  his  ears  intently  towards  the  supposed  point 
of  danger. 

But  the  human  ear  is  not  fitted  so  well  to  reflect  the  vibra- 
tions of  the  air  directly  into  the  passage  leading  to  the  internal 
ear,  as  it  is  to  receive  and  transmit  them  there  through  the  solid 
parts  of  the  head.  But  it  is  supposed  to  be  of  little  use  as  con- 
nected with  the  sensation  of  hearing,  which  is  found  to  be  little 
affected  by  its  loss. 

326.  The  several  parts  of  the  internal  ear  in  man  are  the 
conical-shaped  passage  leading  from  the  external  ear,  about 
nine-tenths  of  an  inch  in  length,  the  tympanum  or  ear-drum, 
with  four  very  small  bones  connected  with  it,  the  Eustachian 
tube,  and  the  labyrinth. 

The  tympanum  is  a  thin  membrane  drawn  like  the  head  of 
a  drum  quite  across  the  passage  leading  from  the  external  ear, 
and  is  designed  to  receive  the  vibrations  from  the  air  with 
which  the  passage  is  filled.  The  four  small  bones  connected 

or  violoncello  serve  ?  Why  are  the  sounds  of  a  music  box  more  distinctly 
heard  when  it  is  placed  on  a  table  than  when  held  in  the  hand  ?  325.  Are 
the  parts  of  the  ear  different  in  different  animals  ?  What  is  the  design  of  the 
external  ear  in  many  animals  ?  Is  the  human  ear  fitted  for  this  purpose  ? 
326.  What  are  the  several  parts  of  the  internal  ear  in  man  ?  What  is  the 
tympanum  ?  What  is  its  design  ?  What  purpose  do  the  four  small  bones 


1C8  NATURAL     PHI  LOSOTIIY. 

with  the  tympanum  are  so  arranged  as  to  transmit  its  vibra- 
tions, somewhat  increased  in  intensity,  to  the  labyrinth,  which 
is  composed  of  a  number  of  bags  or  sacks,  and  semicircular 
canals,  all  of  which  are  filled  with  fluid.  In  this  fluid  are  the  ter- 
minations of  the  auditory  nerves,  which  lead  directly  to  the  brain. 

The  Eustachian  tube  is  a  passage  leading  from  the  upper 
part  of  the  mouth  to  a  small  cavity  behind  the  tympanum, 
called  the  cavity  of  the  tympanum.  This  passage  prevents  any 
unequal  pressure  of  the  air  upon  the  tympanum,  from  varia- 
tions of  the  atmospheric  pressure,  or  from  any  other  cause. 
Sometimes  the  parts  about  this  passage  become  inflamed  so  as 
to  close  it,  which  always  produces  a  sensation  like  that  of  a 
constant  roaring  sound.  This  sensation  almost  every  one  has 
experienced  on  taking  a  severe  cold. 

The  stunning  effect  often  produced  by  the  firing  of  a  cannon 
near  a  person,  is  occasioned  by  the  sudden  and  violent  con- 
cussion of  the  air  against  the  tympanum,  and  through  that 
upon  the  air  within  the  cavity  of  the  tympanum.  It  is  said  it 
may  always  be  avoided  by  having  the  mouth  open  at  the  time 
of  the  explosion;  the  air  is  then  allowed  to  pass  freely  through 
the  Eustachian  tube. 

The  firing  of  cannon  near  windows  will  often  break  the 
glass  by  the  violent  vibrations  of  the  air  against  it ;  but  such 
an  effect  may  be  prevented  usually  by  opening  one  or  more  of 
the  windows  in  each  apartment,  so  as  to  form  a  free  commu- 
nication between  the  air  within  and  that  without. 

327.  The  Voice.  —  The  organs  of  the  voice  consist  of  the 
parts  called  the  thorax,  the  trachea  QY  windpipe,  the  larynx, 
the  mouth,  nose,  and  other  adjacent  parts. 

The  air  during  respiration,  as  we  have  seen  (\  247),  is  con- 
stantly passing  inward  and  outward  through  the  trachea,  by 
the  alternate  expansion  and  contraction  of  the  cavity  of  the 
chest.  Voice  is  always  produced  as  the  air  passes  outward, 
chiefly  by  its  action  on  the  larynx,  which  may  be  considered 
as  the  musical  organ  of  the  voice.  It  is  a  short  tube  with  se- 
veral important  appendages,  situated  at  the  head  of  the  wind- 
pipe, and  is  the  organ  of  the  voice  upon  which  its  pitch  almost 
entirely  depends.  But  in  producing  the  innumerable,  name- 
less modifications  of  sound,  of  which  the  voice  is  capable,  and 
which  are  required  in  ordinary  speech,  other  organs  are  con- 
cerned, as  the  tongue,  palate,  lips,  teeth,  nose,  &c.,  though  the 
distinct  office  of  each  cannot  be  fully  determined. 

connected  with  it  serve  ?  What  is  the  Eustachian  tube  ?  Of  what  use  is  it  ? 
How  may  the  stunning  often  experienced  when  standing  near  a  cannon  that 
is  fired  be  avoided  ?  How  may  the  breaking  of  windows  by  the  firing  of 
cannon  in  the  vicinity  be  to  some  extent  avoided  ?  327.  What  are  the  organs 
of  the  voice  ?  How  are  the  sounds  of  the  voice  produced  ?  What  organ  does 
the  pitch  of  the  voice  chiefly  depend  upon  ?  What  other  organs  are  brought 
into  use  in  producing  the  great  variety  of  sounds  of  which  the  voice  is  capable  ? 


OPTICS.  169 

328.  Ventriloquism  consists  in  imitating  very  accurately  those 
peculiarities  of  sounds,  by  which  we  judge  of  their  distance 
and  position,  with  reference  to  ourselves.  Thus,  when  a  per- 
son hears  a  sound,  he  is  usually  able  to  determine  at  once 
whether  it  was  produced  in  the  same  apartment  with  himself, 
or  in  an  adjoining  apartment,  by  certain  peculiarities  it  pos- 
sesses, which  he  has  learned  from  experience.  Now,  Mr.  A.  is 
in  the  same  room  with  Mr.  B.,  but  is  able  to  give  his  voice  the 
peculiarities  it  would  have  if  coming  from  a  room  adjoining ; 
Mr.  B.,  not  knowing  the  deception,  will  imagine  he  hears  a 
person  in  that  room.  In  the  same  manner,  sounds  may  be  made 
to  appear  to  come  from  any  other  place,  as  from  the  open  air, 
from  the  earth,  from  the  body  of  a  person,  &c.,  by  imitating 
the  peculiarities  which  our  experience  tells  us  might  be  expect- 
ed in  sounds  coming  from  those  places.  Usually  the  ventrilo- 
quist will  direct  the  attention  of  his  audience  to  the  point  from 
which  the  sound  is  expected,  which  very  much  assists  in  the 
illusion. 


CHAPTER  V. 


OPTICS. 

329.  OPTICS  is  that  branch  of  science  which  treats  of  the 
various  phenomena  of  light  and  vision. 

It  is  by  means  of  light  that  we  see  objects;  but  it  has  not  yet 
been  found  possible  to  determine  certainly  what  this  agent 
really  is.  Two  important  theories  concerning  it  have  been 
proposed,  each  of  which  at  different  times  has  been  very 
generally  adopted. 

The  first  of  these  theories  is  that  of  the  illustrious  Newton. 
It  supposes  all  the  phenomena  of  light  and  vision  are  produced 
by  exceedingly  small  particles  which  are  thrown  off  by  lumin- 
ous bodies,  and  which  move  through  space  and  all  transparent 
bodies  with  immense  velocity.  The  particles  are  supposed  to 

Quest  328.  In  what  does  ventriloquism  consist  ?  When  we  hear  a  sound, 
how  do  we  know  whether  it  originates  in  our  own  apartment  or  an  adjoining 
one  ?  If  two  men,  A  and  B,  are  in  the  same  room,  how  may  A  produce  a 
sound  that  to  B  will  appear  to  come  from  an  adjoining  room  ?  How  may  he 
cause  his  voice  to  appear  as  if  coming  from  any  other  place  ?  Why  do  ven- 
triloquists usually  direct  the  attention  of  the  audience  to  the  point  from  which 
the  sound  is  expected  to  come  ?  329.  What  is  treated  of  in  optics  ?  Can  we 
determine  with  certainty  whether  light  is  really  material  ?  What  important 
theories  have  been  proposed  concerning  it  ?  What  is  Newton's  theory  ? 
15 


170  NATURAL     PHILOSOPHY. 

be  constantly  emanating  from  all  self-luminous  bodies,  and 
flying  off  in  every  direction,  and  capable  when  coming  in  con- 
tact with  other  matter,  of  being  reflected,  refracted,  absorbed, 
or  transmitted. 

330.  The  other  theory,  proposed   by  Huygens,  is  usually 
called  the  undulatory  theory.    It  supposes  there  is  everywhere 
diffused   in    space,  even   in  the   most   solid   transparent   bo- 
dies, filling  up  the  interstices  between  their  particles,  an  ex- 
ceedingly subtile  and  elastic  fluid,  in  which   undulations  or 
oscillations  are  excited  by  luminous  bodies,  and  transmitted 
with  immense  velocity,  producing  the  phenomena   of  light, 
much  in  the  same  manner  as  vibrations  in  the  air  ($  295)  pro- 
duce the  phenomena  of  sound.     The  movements  thus  excited 
in  this  subtile  medium  or  ether,  are  readily  propagated  through 
a  vacuum  (which  is  indeed  filled  with  the  ethereal  medium), 
and  through  the  most  solid  transparent  bodies ;  but  in  this  last 
case,  the  elasticity  of  the  medium  being  somewhat  diminished, 
the  movement  is  less  rapid  than  in  free  space. 

331.  These  undulations,  or  oscillations,  however,  are  in  some 
respects  unlike  the  waves  produced  upon  the  surface  of  smooth 
water,  when  a  pebble  is  thrown  into  it,  being  rather  oscillations 
in  the  particles  themselves,  which  are  supposed  to  be  propa- 
gated from  particle  to  particle  in  much  the  same  manner  as 
was  explained  in  the  use  of  the  ivory  balls  (§  104). 

Assuming  that  the  particles  are  spherical, 
we  may  suppose  that  each  one  of  them  be- 
comes alternately  extended  and  depressed, 
horizontally  and  vertically,  as  represented 
in  figure  154 ;  or,  more  properly,  at  its  poles 
and  equator.  Thus,  the  motion  is  an  oscil- 
latory tremulous  motion,  and  may  be  pro- 

pagated  to  distant  particles  without  the  in- 

„'.  termediate  ones  being  moved  out  of  their 

places. 

332.  The  waves  of  light,  like  those  of  sound,  are  transmitted 
in  every  direction,  extending  on  every  side  of  the  luminous 
body,  the  intensity  diminishing  as  the  square  of  the  distance 
increases.     The  sonorous  vibrations  of  a  sounding  body,  as  a 
bell,  it  will  be  recollected,  are  conveyed  to  the  ear,  through  the 
atmosphere,  by  means  of  the  particles  of  the  latter  assuming  a 
similar   wave-like   movement;  and,  in   the   same  manner,  a 
luminous  body,  as  the  sun,  or  a  lamp,  it  is  supposed,  by  exciting 

Quest.  330.  What  is  the  theory  of  Huygens  called  ?  How  are  the  pheno- 
mena of  light  supposed  to  be  produced  on  this  theory  ?  Does  ihe  supposed 
subtile  medium,  called  ether,  pervade  even  solid  bodies?  331.  Are  the 
waves  or  oscillations  of  this  medium  like  waves  upon  the  surface  of  water  ? 
How  may  we  suppose  the  particles  of  ether  alternately  extended  and  de- 
pressed ?  May  these  oscillations  be  propagated  through  the  ether  without 
Us  particles  being  moved  out  of  their  places  ?  332.  Are  the  waves  propa« 


OPTICS.  171 

an  analogous  oscillatory  movement  in  the  universal  ethereal 
fluid,  which  is  propagated  from  particle  to  particle  until  it 
reaches  the  eye,  communicates- to  this  organ  the  sensation  of 
vision,  just  as  the  sonorous  vibrations  produce  in  the  ear  the 
sensation  of  sound.  Darkness,  therefore,  is  occasioned  by  the 
cessation  of  this  oscillatory  movement,  or  the  repose  of  this 
supposed  fluid,  called  ether,  just  as  silence  results  from  the 
cessation  of  the  similar  movements  in  the  air. 

It  is  impossible  in  the  present  state  of  science  to  say  which 
of  these  theories— or  whether  either  of  them — is  true ;  but  the 
undulatory  theory  is  now  almost  universally  adopted  by  scien- 
tific men,  as  it  accords  much  best  with  well-settled  facts.  But, 
in  discussing  the  principles  of  the  science,  we  shall,  notwith- 
standing, continue  to  speak  of  light  as  a  material  substance 
transmitted  from  place  to  place,  and  capable  of  being  thrown 
out  of  its  course,  and  otherwise  variously  acted  on  by  other 
substances  —  language  which  would  seem  to  belong  to  the 
other  theory,  the  theory  of  emission. 

333.  All  visible  bodies  may  be  divided  into  the  two  classes 
of  luminous  and  non-luminous.     The  former  are  those  which 
shine  by  their  own  light,  as  the  sun,  the  stars,  flame,  &c. ;  the 
latter  those  which  have  not  the  power  of  discharging  it  them- 
selves, but  are  capable  of  throwing  back  the  light,  or  part  of 
the  light,  they  receive  from  self-luminous  bodies,  by  which 
they  are  seen,  or  become  visible.   In  every  case  the  light  must 
come  from  a  self-luminous  body,  though  it  may  have  been  se- 
veral times  reflected  before  meeting  the  eye.     When  a  lighted 
candle  is  brought  into  a  dark  room,  the  form  of  the  flame  is 
seen  by  the  light  which  proceeds  directly  from  the  flame  itself; 
but  the  objects  in  the  room  are  seen  by  the  light  which  they 
receive  from  the,  candle,  and  again  thrown  back  to  the  eye. 
Other  objects  still  there  may  be  in  the  room,  which  are  so  situ- 
ated as  not  to  receive  any  light  directly  from  the  candle,  but  be- 
come visible  by  the  light  reflected  from  the  wall  and  ceiling, 
&c.  of  the  room. 

Light  is  emitted  from  every  visible  point  of  a  luminous  or  an 
illuminated  body,  and  in  every  direction. 

334.  Transparent  bodies  are  such  as  transmit  light  freely,  so 
that  objects  may  be  seen  through  them.     Bodies  that  transmit 
the  light,  but  not  sufficiently  to  render  objects  visible  through 
them,  are  said  to  be  translucent.    Substances  that  do  not  permit 
light  to  pass  through  them  in  any  degree  are  called  opake.    But 
this  term  is  sometimes  used  to  mean  the  same  as  non-luminous. 

gated  in  every  direction  ?  What  is  darkness  ?  Is  the  undulatory  theory  of  light 
now  generally  adopted  ?  333.  Into  what  two  classes  may  all  visible  bodies 
be  divided  ?  What  are  luminous  bodies  ?  How  are  non-luminous  bodies 
seen,  as  no  light  is  emitted  by  them  ?  Must  the  light  always  originate  from 
a  luminous  body  ?  Is  light  emitted  from  every  point  of  a  luminous  body  ? 
334.  What  are  transparent  bodies  ?  When  are  bodies  said  to  be  translucent? 
When  are  they  said  to  be  opake  ? 


172  NATURAL     PHILOSOPHY. 

335.  A  ray  is  merely  a  small  portion  of  light ;  the  smallest 
portion  that  can  be  intercepted  or  examined.  A  large  ray,  or  a 
combination  of  rays,  is  sometimes  called  a  pendlor  beam  of  Light. 

336.  The  rays  of  light  may  be  parallel,  or  they  may  be  con- 
vergent, or  divergent.     Parallel  rays,  as  the  term  implies,  are 
everywhere  equally  distant  from  each  other;  but  convergent 
rays  approach  each  other  as  they  advance,  while  divergent 
rays  separate. 

The  surface  of  a  body  may  be  considered  as  made  up  of  a 
great  multitude  of  very  small  points,  and  from  every  one  of 
these  in  a  luminous  body  the  rays  of  light  are  thrown  off;  con- 
sequently, the  rays  from  a  luminous  body  near  us  must  always 
be  divergent ;  that  is,  they  must  always  separate  farther  and 
farther  as  they  advance. 

Thus,  let  A,  figure  155,  represent 
a  lighted  candle,  and  P  and  P'  two 


pencils  of  rays  emanating  from  points 
in  it;  it  will  be  seen  that  as 


as  they  ad- 
vance they  diverge  or  separate  more 
and  more  from  each  other.  In  this 
case  we  have  represented  the  rays 

thrown  off  from  two  points  only  —  and  indeed  only  a  part  of 
those  from  each  of  these  points,  since  many  more  rays  both 
above  and  below  those  shown  in  the  figure,  proceed  from  the 
same  points.  To  obtain  a  correct  idea  of  what  really  takes 
place,  it  is  necessary  to  recollect  that  pencils  of  rays  are  pro- 
ceeding in  this  manner  from  every  point  of  the  flame  of  the 
candle,  crossing  each  other  in  every  direction. 

As  a  necessary  result  of  this  divergence  of  the  rays  of  light, 
it  must  at  length  become  so  expanded  as  to  cease  to  affect  the 
eye ;  and  the  !  >ody  from  which  it  emanates  will  then  be  in- 
visible. 

Rays  of  light  from  a  luminous  body  can,  strictly  speaking, 
never  be  parallel ;  but,  when  their  source  is  exceedingly  dis- 
tant, as  in  the  case  of  rays  from  the  sun  or  any  other  celestial 
body,  it  is  evident  they  may  be  considered  so. 

The  direct  rays  of  a  luminous  body  can  never  converge;  in 
order  to  be  convergent,  they  must  first  be  reflected  or  refract- 
ed, as  will  be  seen  hereafter. 

337.  The  passage  of  light  is  progressive,  it  requiring  about 
16|  minutes  to  cross  the  earth's  orbit,  or  about  8£  minutes  to 
come  from  the  sun  to  the  earth.  This  is  best  determined  by 

Quest.  335.  What  is  a  ray  of  light?  What  is  a  pencil,  or  learnt  336. 
When  are  rays  said  to  be  parallel  ?  Convergent?  Divergent  ?  What  may 
the  surface  of  a  body  be  supposed  to  be  made  up  of?  Is  light  emitted  from 
each  point  ?  Will  the  rays  from  a  body  near  us  always  be  divergent  ?  How 
is  this  shown  in  figure  155  ?  May  rays  from  a  very  distant  body  be  consi- 
dered parallel  ?  Can  the  direct  rays  from  a  luminous  body  ever  converge  ? 
337.  Is  the  passage  of  light  progressive  ?  How  long  is  light  in  corning  from 
the  sun  ?  By  what  means  is  this  determined  ?  What  is  the  velocity  of  hght 


OPTICS.  173 

means  of  the  eclipses  of  Jupiter's  satellites,  which  are  con- 
stantly taking  place. 

The  earth  and  Jupiter,  in  their 
revolutions  round  the  sun,  are 
sometimes  both  on  the  same  side 
of  that  luminary,  and  at  others 
they  are  on  opposite  sides.  In 
figure  156,  let  S  be  the  sun,  E  the 
earth,  and  J  Jupiter;  both  the 
earth  and  Jupiter  being  now  on 
the  same  side  of  the  sun.  The 
light  from  Jupiter,  in  coming  to 
the  earth,  will  now  have  to  pass 
through  the  distance  J  E  only. 
But,  in  a  little  more  than  six 
months  after  the  earth  and  Jupi- 
ter are  in  the  position  above  sup- 
posed, the  earth  will  have  advanced 
Fig-  156.  to  E',  and  Jupiter  to  J' ;  they  will 

then  be  on  opposite  sides  of  the  sun ;  and  the  light  from  Jupiter,  to  reach 
the  earth,  will  have  to  traverse  the  whole  distance  J'  E',  which  is  greater 
than  J  E  by  the  distance  A  E',  or  the  diameter  of  the  earth's  orbit. 

Now,  when  these  two  bodies  are  in  the  position  last  indicated,  in  reference 
to  the  sun,  the  eclipses  of  Jupiter's  moons  are  uniformly  found  to  take 
place  about  16f  minutes  later  than  when  they  are  in  the  first  position; 
that  is,  when  they  are  on  the  same  side  of  the  sun.  This  shows  that  light 
is  this  period  of  time  in  passing  from  A  to  E' ;  or,  about  85  minutes  in 
passing  from  S  to  E',  or  from  the  sun  to  the  earth. 

The  velocity  of  light  is  therefore  about  192,000  miles  a  second, 
which  is  evidently  so  great  that  we  are  absolutely  incapable 
of  measuring  the  time  that  is  required  for  light  to  pass  any  dis- 
tance over  the  earth's  surface.  Indeed,  in  one  second  it  would 
pass  no  less  than  8  times  quite  around  the  earth. 

The  progressive  motion  and  the  velocity  of  light  are  also 
shown  by  the  phenomena  of  aberration,  which,  however,  can- 
not be  here  explained. 

338.  In  the  same  medium,  light  always  moves  in  a  straight 
line;  it  is,  therefore,  impossible  to  see  through  a  bent  tube. 

339.  When  light  falls  upon  an  opake  object,  it  is  intercepted, 
and  darkness,  more  or  less  intense,  is  produced  on  the  opposite 
side,  called  a.  shadow,  or  umbra.  This  is  always  surrounded  by 
a  border  less  dark  than  the  shadow  itself,  which  is  called  the 
penumbra.   It  is  occasioned  by  the  interception  of  a  part  of  the 
light  from  the  luminous  body.  An*eye  situated  in  the  penumbra 
will  always  be  able  to  see  a  part,  and  only  a  part,  of  the  lumin- 
ous body. 

per  second  ?  How  many  times  would  light  pass  round  the  earth  in  a  second  f 
!38.  Does  light  always  move  in  a  straight  line  in  the  same  uniform  medium  ? 
339.  What  is  a  shadow  ?  By  what  is  the  shadow  always  surrounded  ?  How 
is  this  occasioned  ?  Will  an  observer  see  the  whole  of  a  luminous  body  when 
his  eye  is  in  the  penumbra  ? 


174  NATURAL     PHILOSOPHY. 


REFLECTION     OF    LIGHT. 

340.  When  rays  of  light,  on  coming  in  contact  with  an  opake 
body,  are  thrown  back,  they  are  said  to  be  reflected ;  and  in 
its  reflections  it  is  governed  by  the  same  laws  as  perfectly 
elastic  solid  bodies.  (§  62). 

The  ray,  before  it  comes  in  contact  with  the  reflecting  sur- 
face, is  called  the  incident  ray;  after  it  rebounds  from  the  sur- 
face, it  is  called  the  reflected  ray.  Now,  if  we  admit  a  single 
ray  of  light  into  a  darkened  chamber,  and  cause  it  to  strike 
perpendicularly  against  a  reflecting  surface,  it  is  thrown  or  re- 
flected directly  back ;  but  if  the  reflecting  substance  is  held  a 
little  inclined  to  the  ray,  it  is  reflected  obliquely,  and  a  lumin- 
ous spot  is  seen  on  the  wall  where  the  ray  strikes. 

Let  us  suppose  AB,  figure  157,  to 
be  the  reflecting  body,  EC  the  inci- 
dent ray,  and  C  D  the  reflected  ray. 
If,  now,  at  C,  the  point  of  contact,  we 
erect  a  perpendicular,  C  P,  then  E  C  P 
will  be  the  angle  of  incidence,  and 
,„-     ^     ^       =B  P  C  D  the  angle  of  reflection ;  and  these 
/^  \        two  angles  will  always  be  equal. 

-A!  B'  it  is  riot  necessary  that  the  reflect- 

Pig.  157.  ing  surface  should  be  a  plane ;  it  may 

be  concave,  as  a  b,  or  convex,  as  A'  F,  and  yet  the  ray  will 
obey  the  same  law. 

341.  A  good  reflecting  surface  is  called  a  mirror  or  speculum. 
Mirrors  are  made  usually  of  polished  metal,  or  of  glass,  covered 
on  the  back  with  an  amalgam  of  tin. 

342.  A  considerable  portion  of  light  is  always  lost  on  coming  in  contact 
with  reflecting  surfaces,  no  mirror  being  capable  of  throwing  back  or  re- 
fleeting  all  the  light.  The  more  inclined  the  incident  ray  is  to  the  reflect- 
ing  surface,  the  greater  will  be  the  proportion  reflected.  Thus,  it  is  found 
that  when  the  angle  of  incidence  is  85°,  from  the  surface  of  water  about 
501  out  of  1000  parts  are  reflected ;  but  when  the  angle  of  incidence  is 
only  20°,  then  only  18  out  of  1000  rays  are  reflected.     When  the  reflector 
is  transparent,  as  a  glass  plate,  much  more  light  is  reflected  from  the  se- 
cond than  from  the  first  surface ;  and  this  proportion  is  increased  when 
the  back  is  coated  with  some  resinous  cement  or  black  paint ;  or,  better 
still,  some  metallic  amalgam,  as  in  the  common  looking-glass.     In  this 
case  the  reflections  become  very  vivid,  and  the  images  of  objects  bright. 

343.  Mirrors  are  made  of  various  forms,  of  which  the  chief 
are  the  plane,  the  concave,  and  the  convex.     The  common  look- 
ing-glass is  an  instance  of  a  plane  mirror;  it  consists  simply  of 

Quest.  340.  When  is  light  said  to  be  reflected  ?  What  is  meant  by  the 
incident,  and  what  by  the  refected  ray  ?  What  are  the  angles  of  incidence 
and  reflection  in  figure  157  ?  Must  the  reflecting  surface  be  a  plane  surface  ? 
341.  What  is  a  mirror  ?  342.  Will  all  the  light  be  reflected  ?  343.  What 
different  forms  of  mirrors  are  mentioned  ?  What  is  the  form  of  the  plans 


OPTICS.  175 

a  plain,  level,  polished  surface.  The  concave  mirror  is  a  por- 
tion of  the  inside  surface  of  a  hollow  sphere,  —  usually  but  a 
small  portion  of  the  whole  sphere.  The  convex  mirror,  in  like 
manner,  is  a  portion  of  the  external  surface  of  a  sphere.  A 
line  perpendicular  to  the  centre  of  a  concave  or  convex  mirror 
is  called  its  axis. 

344.  Rays  of  light  reflected  from  a  plane  mirror  always  re- 
tain the  same  direction  with  reference  to   each   other  after 
reflection  as  they  possessed  before.    Thus,  rays  parallel  before 
reflection  will  be  reflected  parallel ;  and  rays  convergent,  or 
divergent  before  reflection,  will  be  reflected  convergent  or 
divergent,  as  the  case  may  be.     This  may.  be  more  clearly  un- 
derstood by  referring  to  figure  158. 

Let  A  B  be  a  plane  mir- 
ror, and  C  D  two  parallel 
rays;  after  reflection  they 
take  the  direction  cd,  and 
to  the  eye  they  will  ap- 
pear to  come  in  the  direc- 
tion C'  D'.  Diverging  rays 
proceeding  from  a  point, 
Fig.  iss.  E,  will  be  reflected  in  the 

direction  eee,  and  will  appear  to  come  from  the  point  E'  behind 
the  mirror.  So  will  the  converging  rays,  FFF,  be  likewise 
reflected  converging ;  and  they  will  meet  in  the  point  G,  just 
as  if  they  originated  in  the  direction  F'F7  F'.  The  effect  of  re- 
flection in  every  case  is  to  throw  the  apparent  origin  of  the 
rays  on  the  opposite  side  of  the  mirror,  since  objects  always 
appear  to  the  eye  to  be  situated  in  the  direction  of  the  rays 
which  finally  reach  that  organ. 

345.  Rays  reflected  from  a  concave  mirror  are  in  general 
made  to  converge ;  or  if  they  are  very  divergent,  they  are  made 
to  diverge  less.     Parallel  rays  are  made  to  converge  to  a  point 
called  the  principal  focus  of  the  mirror,  which  is  about  midway 
between  the  centre  of  the  sphere  of  which  the  mirror  is  a  part, 
and  the  surface  of  the  mirror. 

Let  A  E  B,  figure  158  a,  be  a  * 

concave  mirror;  C,  the  centre      p*~ : * 

of  the  sphere  of  which  the  mirror      f/'-^V • e 

forms  a  part;  and  defgh  pa-   El — ^jj^ «& f 

rallel  rays.  After  reflection  they      \^s    £ 

will  be  collected  in  the  focus,     J^— "h, 

F,  where  the  light  and  heat  of  B^ 

all  the.  rays  will  of  course  be  Fls-  isso. 

mirror  ?  The  convex  mirror  ?  The  concave  ?  What  is  the  axis  of  a  convex 
or  concave  mirror  ?  ,  344.  Do  rays  of  light  reflected  from  a  plane  mirror 
always  retain  the  same  direction  with  reference  to  each  other  after  reflection 
as  before  ?  How  is  this  illustrated  by  figure  158  ?  345.  How  are  rays  re- 
flected from  the  concave  mirror  ?  What  is  the  focus  of  a  concave  mirror  ? 


176  NATURAL     PHILOSOPHY. 

concentrated.  E  F  is  called  the  focal  distance,  or  the  principal 
focal  distance  of  the  mirror. 

From  what  has  been  said  it  is  evident  that  rays  emanating 
from  the  focus  F  will  be  reflected  parallel. 

. ^          It  is  evident  the  concave  mir- 

A\  a   ror  may  be  considered  as  a  mul- 

— b    titude  of  plane  mirrors  inclined 
c    towards  each  other.  Let  A  B  C  D, 
figure  159,  be  four  plane  mirrors 

v  A  arranged  on  the  circumference 

Fig.  159.  of  a  circle,  and  abed,  several 

parallel  rays;  these  rays  will  strike  the  mirrors  at  different 
angles,  and  obey  the  usual  law  (§  340) ;  but  they  will  all  be  re- 
flected very  nearly  to  the  same  point,  F. 

Rays  converging  before  reflection  are,  by  reflection  from  the 
concave  mirror,  made  more  convergent;  and  their  focus  is 
nearer  the  mirror  than  F,  the  focus  of  parallel  rays. 

346.  Diverging  rays  will  be  made 
less  divergent,  or  parallel,  or  con- 
vergent, according  to  their  compara- 
tive   divergency    before    reflection. 
Suppose  them  to  be  radiated  from  a 
luminous  body  situated  at  P,  figure 
160;  then,  after  reflection,  the  focus 

will  be,  not  at  F,  as  before,  but  at  /,  Fig.  150. 

a  point  nearer  the  centre,  C.  If,  now,  the  radiant  point,  P,  be 
made  to  approach  the  centre  C,  the  focus  /will  also  gradually 
approach  to  C  ;  and  when  the  radiant,  P,  reaches  that  point,  its 
rays,  it  is  evident,  will  be  reflected  directly  back.  If  P  is  car- 
ried still  nearer  the  mirror  A  B  than  C,  /  will  recede  beyond  C 
to  the  right,  and  the  two  foci  will  at  length  change  places. 
The  two  points,  P  and  /,  are  therefore  sometimes  called  conju- 
gate foci,  to  represent  their  intimate  relation  to  each  other.  If, 
however,  the  luminous  body  be  placed  nearer  the  mirror  than 
F,  which  is  the  focus  of  parallel  rays,  its  rays  will  be  reflected, 
not  parallel,  but  divergent,  as  though  they  emanated  from 
some  point  behind  the  mirror. 

347.  The  effect  of  the  convex  mirror  is  directly  the  reverse 
of  that  of  the  concave  mirror ;  it  separates  the  rays  after  re- 
flection. 

Where  is  it  situated  ?  What  is  ihe  focal  distance  of  a  concave  mirror  ?  What 
may  the  concave  mirror  be  considered  as  made  up  of?  346.  How  will 
diverging  rays  be  reflected  by  the  concave  mirror  ?  Will  the  focus  of 
diverging  rays  be  the  same  as  if  they  were  parallel  ?  If  the  radiant  point,  P, 
figure  160,  is  made  to  approach  the  mirror,  how  will  the  focus  be  affected? 
If  the  luminous  body  is  placed  nearer  the  mirror  than  its  principal  focus, 
what  will  be  the  effect  ?  347.  What  is  the  effect  of  the  convex  mirror  upon 
rays  of  light  ?  From  what  point  will  the  rays  appear  to  emanate  ?  What  is 
this  point  called  ? 


OPTICS, 


177 


Thus,  let  a  b  cde,  figure  161, 
be  several  parallel  rays  inci- 
dent upon  a  convex  mirror, 
A  B,  of  which  C  is  the  centre 
of  convexity  ;  they  will  be  re- 
c  fleeted  according  to  the  ge- 
neral law,  making  for  each 
ray  the  angle  of  incidence 
equal  to  the  angle  of  reflec- 
tion ;  the  ray  a  will  therefore 
take  the  direction  of  a/,  b  that 
of  b',  d  that  of  d',  and  e  that 
of  e'.  They  will  all  appear 

after  reflection  to  come  from  the  same  point,  F,  behind  the 
mirror,  which  is  therefore  called  the  virtual,  or  apparent  focus. 
In  the  case  of  converging  rays,  the  distance  of  F  from  the 
mirror  will  be  greater,  and  in  that  of  diverging  rays,  Jess,  than 
for  parallel  rays. 

348.  When  a  pencil  of  rays  falls  upon  a  concave  surface, 
after  reflection  it  is  evident  they  must  intersect  each  other, 
and  the  points  of  intersection  will  constitute  a  curved  line, 
which  is  termed  a  caustic,  or  sometimes  a  caustic  by  reflection. 

To  exhibit  this  curve,  fill  a  wine-glass  K_ 
nearly  full  with  milk,  and  place  it  so  that 
it  may  receive  the  direct  light  of  the  sun 
or  of  a  lamp  as  represented  in  figure  162. 
The  light  will  be  reflected  from  the  con- 
cave surface  of  the  glass,  and  form  the 
curve  upon  the  surface  of  the  milk.  The 
same  effect  will  be  produced  if  a  piece 
of  card  is  fitted  accurately  into  the  glass 
a  little  below  the  top. 

Fig.  162. 

349.  Formation  of  Images  by  Reflection.  —  The  surface  of  a 
body,  as  we  have  seen,  may  be  considered  as  made  up  of 
points ;  and  to  see  this  surface  is  to  see  all  these  points,  each 
of  its  proper  colour,  and  in  its  proper  position,  with  reference 
to  all  the  others.    So,  to  form  an  image  of  an  object,  is  to  form 
an  image  of  all  its  points  in  their  natural  position ;  and  an 
image  of  a  point  is  formed  when  all,  or  only  a  part  of  the  rays 
emanating  from  it  are  again  collected  and  reflected  to  the  eye. 

350.  There  are,  however,  two  kinds  of  images  of  objects, 
which  in  some  respects  are  quite  different  from  each  other. 
The  first  kind  is  merely  a  reflection  to  the  eye  of  a  portion  of  the 
light  that  proceeds  from  an  object,  as  the  image  of  an  object  seen 
in  a  common  mirror  or  looking-glass.  Here  no  screen  is  needed, 

Quest.  348.  What  is  illustrated  in  figure  162  ?  349.  If  the  surface  of  a 
body  may  be  considered  as  made  up  of  many  points,  what  is  it  to  see  a 
body  ?  350.  How  many  kinds  of  images  of  bodies  are  there  ?  What  is 
the  first  kind  ?  How  must  the  observer  be  situated  in  reference  to  the 


178  NATURAL     PHILOSOPHY. 

but  the  observer  must  be  so  situated  as  to  see  the  surface  of  the 
reflector  behind  which  the  image  seems  to  be  situated.  The 
second  kind  of  image  is  generally  formed  upon  a  screen  of  some 
kind,  as  a  piece  of  paper,  or  cloth,  or  the  surface  of  ground 
glass.  In  this  case  the  reflecting  surface  may  be  entirely  con- 
cealed from  view;  it  is  only  necessary  that  the  surface  on 
which  the  image  is  formed  should  be  visible.  To  illustrate 
more  clearly  what  is  meant,  let  a  person  observe  the  reflection 
of  a  window  on  the  opposite  side  of  a  room  in  a  common  look- 
ing-glass; this  is  an  image  of  the  first  kind.  Then  let  him 
darken  all  the  windows  in  the  room  but  one,  and  hold  a  pair 
of  spectacles  from  10  to  20  inches  from  the  wall  on  the  side  of 
the  room  opposite  this  window,  so  that  the  light  from  the  win- 
dow may  pass  through  one  of  the  glasses  to  the  wall.  As  soon 
as  he  gets  the  spectacles  at  the  proper  distance  from  the  wall, 
a  diminished  but  most  beautiful  image  of  the  window  will  be 
seen  upon  the  wall,  which  in  this  case  constitutes  the  screen. 
This  is  the  second  kind  of  image  referred  to.  In  the  first  in- 
stance, the  image  of  the  window  is  seen  only  by  looking  on 
the  face  of  the  mirror;  and,  indeed,  as  stated  above,  it  con- 
sists merely  of  the  light  from  the  window  reflected  to  the 
eye ;  but,  in  the  second,  an  image  of  the  object  is  actually 
formed  upon  the  wall  of  the  room,  and  the  eye  observes  it  as 
a  new  object. 

351.  From  what  has  already  been  said  of  the  plane  mirror, 
(5  344),  it  necessarily  follows  that  the  image  of  an  object  seen 
in  it  will  always  appear  erect  and  of  the  natural  size,  and 
situated  just  as  far  behind  the  mirror  as  the  object  is  in  front 
of  it.  Let  it  be  constantly  borne  in  mind  that  the  light  by 
which  an  object  is  seen  emanates  from  each  point  of  that 
object,  and  diverges  as  it  advances  until  it  reaches  the  eye. 

Thus,  in  figure  163,  let  ABC  be 
three  points  of  an  object,  as  a  cross, 
which  is  seen  by  the  eye,  E.  From 
these  three  points  (as  well  as  from 
every  other  point  of  the  object)  rays 
are  thrown  off  in  every  direction, 
diverging  as  they  proceed;  but  a 
small  pencil  of  those  from  each  point 

is  intercepted  by  the  eye,  and  by  this  pencil  that  individual 
point  is  seen.  Thus,  from  each  point  of  an  object,  a  cone  of 
rays  may  be  supposed  to  be  formed,  the  base  of  which  is  at  the 
pupil  of  the  eye,  and  the  apex  at  the  point  from  which  the  rays 

mirror,  in  order  to  see  the  image  ?  What  is  an  image  of  the  second  kind 
usually  formed  upon  ?  May  an  image  of  this  kind  be  observed  when  the 
mirror  itself  is  entirely  concealed  from  view  ?  How  may  the  two  kinds  of 
images  be  shown  by  means  of  a  mirror  and  a  common  burning-glass,  in  a 
room  with  a  single  window  ?  351.  Where  will  the  image  of  an  object  seen 
in  a  plane  mirror  always  appear  to  be  situated  ?  By  what  is  each  point  of  an 
object  seen  ?  Must  each  point  be  seen  by  its  own  independent  cone  of  rays  I 


OPTICS. 


179 


emanate.  Each  point,  therefore,  of  the  object,  is  seen  by  its 
own  independent  cone  of  rays ;  and,  to  see  the  whole  assem- 
blage of  points  of  the  surface  of  the  body  next  the  eye  of  the 
observer,  is,  as  before  observed,  to  see  the  object. 

352.  It  will  be  easy  now,  it  is  believed,  to  understand  the 
manner  in  which  images  are  produced  by  the  plane  mirror. 
As  this  mirror  reflects  diverging  rays  equally  divergent  as  be- 
fore reflection  (§  344),  the  only  effect  of  the  mirror  on  the  cones 
of  rays  from  the  several  points  of  the  object  will  be  to  turn 
them  all  precisely  alike  out  of  their  course,  and  thus  change 
the  apparent  place  of  their  origin ;  or,  in  other  words,  change 
the  apparent  place  of  the  object. 

Let  A  B,  figure  164,  be  a  plane  mirror ; 
MN,  an  object  placed  before  it;  and  E, 
the  eye  of  the  observer ;  then,  of  all  the 
rays  emitted  from  the  two  points  M  and 
N,  and  subsequently  reflected  from  the 
mirror,  those  only  can  reach  the  eye 
which  are  so  situated  with  respect  to  it, 
and  the  points  M  N,  that  the  angles  of  in- 
cidence and  reflection  will  be  equal.  Sup- 
pose the  cones  of  rays,  M  DP  and  NGH, 
to  be  so  situated ;  they  will  be  reflected  to 
the  eye  precisely  as  diverging  as  before; 
and  if  they  are  continued  backward,  they  will  seem  to  originate 
in  the  points  m  and  n  respectively.  And  as  the  rays  diverge 
equally  before  and  after  reflection,  the  points  m  and  n  will  appear 
just  as  far  behind  the  mirror  as  M  and  N  are  in  front  of  it.  The 
image  of  an  object,  therefore,  seen  in  a  plane  mirror,  is  always 
of  the  same  size  as  the  object,  and  is  situated  just  as  far  behind 
the  mirror  as  the  object  is  in  front  of  it. 

353.  Images  of  the  first  kind  (\  350), 
are  formed  by  concave  and  convex  mir- 
rors in  the  same  manner  as  by  plane 
ones;  but  those  produced  by  the  con- 
vex mirror  are  always  smaller  than  the 
object.     The  reason  of  it  may  be  shown  A 
without  difficulty.     Let  A  B,  figure  165, 
be  a  convex  mirror,  and  D  F  an  object 
in  front  of  it.  If,  now,  rays  are  supposed 
to  emanate  from  the  object,  a  portion  of 

them  from  each  point  will  be  intercepted  \j 

by  the  mirror,  and  reflected  to  the  eye  »c 

at  E ;  but,  as  they  are  made  by  the  mir-  Fig.  165. 

Quest.  352.  What  will  be  the  effect  of  the  plane  mirror  upon  the  supposed 
cone  of  rays  from  each  point  of  an  object  ?  What  is  the  design  of  figure  164  ? 
353.  May  images  of  the  first  kind  be  formed  by  concave  and  convex  mirrors  ? 
Will  the  image  of  an  object  seen  in  a  convex  mirror  be  smaller  or  larger  than 
the  object  ?  Where  will  it  appear  to  be  situated  ? 


\  i 


180 


NATURAL     PHILOSOPHY. 


ror  to  diverge  more  than  before  reflection,  they  will  appear  to 
emanate  from  a  point  behind  the  mirror  nearer  to  it  than  the 
object  is  in  front.  The  point  D  will  appear  at  D',  and  the  point 
F  at  F' ;  the  image  being  smaller  than  the  object.  The  points 
D'  and  F'  will  always  be  situated  in  lines  drawn  from  D  and  P 
to  C,  the  centre  of  convexity  of  the  mirror. 

354.  When  an  object  is 
placed  nearer  a  concave  mir- 
ror than  its  principal  focus, 
an  image  is  formed  by  it  in 
the  same  manner;  but  it  is 
O  larger  than  the  object.  Let 
A  B,  figure  166,  be  a  concave 
mirror,  and  M  N  an  object  in 
front  of  it,  nearer  than  its 
principal  focus.  The  rays, 
after  reflection,  being  less 
divergent  than  before,  the 

image  of  the  object  will  appear  farther  from  the  mirror  than 

the  object  is,  and  larger.     The  rays  from  the  points,  M  and  N, 

will  appear  to  originate  at  M'  and  N',  in  lines  drawn  from  the 

centre,  C,  through  M  and  N  respectively. 
355.  By  means  of  the  concave 

mirror,  images  may   be  formed 

which  we  have  described  above 

(§350),  as  images  of  the  second 

kind.  Let  E  A,  E  G,  and  E  B,  figure 

167,  be  three  rays  emitted  from 

the  point,  E,  of  an  object,  E  D,  in 

front  of  a  concave  mirror,  A  B, 

and  farther  from  it  than  C,  its  cen- 


Fig.  166. 


Fig.  167. 


tre  of  concavity.  The  ray,  EG,  being  incident  upon  the  mirror 
at  its  centre,  will  be  reflected  just  as  much  below  the  axis  G  H 
as  EG  is  above  it;  and  to  the  same  point  will  both  the  other 
rays  from  E  be  reflected.  An  image  of  the  point  E,  therefore, 
will  be  formed  at  E',  a  little  below  the  axis,  HG;  and,  in  the 
same  manner,  an  image  of  the  point  D  will  be  formed  at  D',  a 
little  above  the  axis.  So,  the  images  of  the  several  points  be- 
tween E  and  H  will  be  arranged  in  their  proper  order  below 
the  axis,  while  those  of  the  part  D  H  will  be  above  the  axis,  the 
whole  forming  an  inverted  image  of  the  object,  E'D'. 

The  size  of  the  image  E'D'  will  be  as  much  less  than  that 
of  the  object.  ED,  as  its  distance  from  the  mirror  is  less.  That 

Quest.  354.  Where,  in  reference  to  the  concave  mirror,  must  an  object 
be  situated  in  order  that  an  image  of  this  kind  may  be  seen  in  it  ?  Will  it 
be  larger  or  smaller  than  the  object  ?  355.  In  figure  167,  if  an  object  be 
placed  at  E  D,  where  will  the  image  of  the  points,  E  and  D,  be  formed  ? 


OPTICS.  181 

is,  the  size  of  the  image  will  be  to  that  of  the  object,  as  the  dis- 
tance of  the  image  from  the  mirror  is  to  the  distance  of  the 
object. 

If  the  object  is  placed  at  E'  D',  its  image  will  be  painted  on  a 
screen  situated  at  E  D,  and  will  be  as  much  magnified  as  it  was 
diminished  in  the  former  instance.  In  this  case  also  the  image 
will  be  inverted  in  reference  to  the  object.  In  both  cases,  it 
will  be  observed,  the  image  and  object  occupy  the  places  of  the 
conjugate  foci  (§  346)  of  the  mirror. 

If  an  object  is  placed  exactly  in  the  focus  of  parallel  rays,  no 
image  can  be  produced,  since  all  the  rays  will  be  reflected 
parallel  (§  345);  if  placed  nearer  than  this,  they  will  be  made  to 
diverge  after  reflection,  and  of  course  no  image  can  be  formed 
in  front  of  the  mirror. 

356.  Experiments  illustrating  these  principles  can  easily  bo 
performed  by  means  of  a  lighted  candle  in  a  dark  room,  and 
any  concave  mirror  of  sufficient  size.  Having  placed  the  mirror 
in  a  proper  position  upon  a  table,  let  the  candle  be  placed  near 
it  as  at  D'  E',  figure  167,  but  a  little  one  side  of  its  axis ;  then 
let  a  screen,  as  a  sheet  of  white  paper,  be  held  at  a  distance,  as 
at  ED.  If  a  perfect  inverted  image  of  the  flame  is  not  at  once 
seen  upon  the  paper,  it  will  be  because  its  distance  from  the 
mirror  is  either  too  little  or  too  great,  and  it  is  to  be  moved 
backward  and  forward  until  the  image  becomes  distinct.  It 
will  be  much  larger  than  the  flame. 

Let  the  candle  now  be  removed  to  a  distance  from  the  mirror, 
and  placed  at  E  D,  the  centre  of  the  blaze  being  at  the  same 
height  as  the  centre  of  the  mirror,  and  let  the  sheet  of  paper  be 
held  at  the  other  conjugate  focus,  E'  D'.  In  order  that  the  light 
from  the  candle  may  not  be  intercepted  by  the  paper,  the  candle 
must  be  placed  a  little  on  one  side  of  the  mirror's  axis,  and  the 
paper  held  a  little  on  the  other  side.  The  distance  of  the  paper 
from  the  mirror  must  also  be  accurately  adjusted  in  order  to 
obtain  a  perfectly  distinct  image.  As  before,  the  image  will  be 
inverted,  but  it  will  be  much  smaller  than  the  object  itself.  If 
the  size  of  the  images  in  the  two  cases  are  accurately  measured, 
they  will  be  found  to  be  just  in  proportion  to  the  distances  of 
the  screen  from  the  mirror  where  they  were  formed  re- 
spectively. 

357.  By  means  of  a  concealed  concave  mirror  of  a  large 
size,  various  illusions  have  sometimes  been  practised. 


Will  the  image  be  erect  or  inverted  ?  How  will  the  size  of  the  image  com- 
pare with  that  of  the  object  ?  If  the  object  were  placed  at  E'  D',  where 
would  the  image  be  formed  ?  Would  it  be  larger  or  smaller  than  the  object  ? 
Will  an  image  be  formed  when  the  object  is  in  the  focus  of  parallel  rays  ? 
356.  How  may  experiments  be  performed  to  illustrate  the  mode  in  which 
images  are  formed  by  means  of  the  concave  mirror  ?  357.  How  may  the 
image  of  an  object  be  formed  so  as  to  be  visible  to  the  observer  when  both 
the  mirror  and  object  are  concealed  ? 

16 


182 


NATURAL     PHILOSOPHY. 


- 168. 


LetGF,  figure  168,  be 
a  large  concave  mirror, 
not  less  than  a  foot  in 
diameter,  and  let  A  B  be 
a  portion  of  a  screen  con- 
cealing it  from  the  direct 
view  of  the  observer,  but 
having  an  opening  in  it 
exactly  in  front  of  the 
mirror.  An  object,  as  a  bunch  of  flowers,  is  then  placed  in- 
verted at  C,  and  strongly  illuminated  by  a  lamp,  which,  how- 
ever, must  not  cast  its  light  upon  the  mirror.  Both  the  flowers 
and  the  lamp  are  also  concealed  from  the  spectator,  whose  eye 
is  supposed  to  be  at  E.  He  will,  however,  see  a  beautiful  image 
of  the  flowers  erect  at  D,  in  the  opening  in  the  screen;  but, 
upon  his  attempting  to  lay  hold  of  them,  a  dagger,  or  some 
other  object,  to  his  utter  consternation,  instantly  takes  their 
place.  This  is  done  by  a  person  behind  the  screen  instantly 
removing  the  flowers,  and  substituting  a  dagger  in  their  place. 

358.  Besides  the  mirrors  described  above,  others  of  different 
forms  are  sometimes  constructed,  but  they  always  form  dis- 
torted images  of  objects.    Of  this  kind  are  cylindrical  and 
conical  mirrors,  the  names  of  which  sufficiently  indicate  their 
forms.  The  effect  of  a  cylindrical  mirror  may  be  seen  by  taking 
a  bright  sheet  of  tin-plate  in  the  two  hands,  and  slightly  bend- 
ing its  two  opposite  sides  backward,  and  observing  the  image 
of  the  face  in  it.    Every  part  of  the  face  will  appear  of  the  full 
length,  but  will  be  diminished  in  breadth,  giving  the  whole  a 
ludicrous  aspect.     If  the  upper  and  lower  sides  of  the  plate  are 
bent  backward,  the  reverse  effect  will  be  produced ;  the  parts 
of  the  face  will  appear  of  the  usual  breadth,  but  greatly  dimi- 
nished in  length. 

359.  Sometimes  distorted  pictures  of  objects 
are  made,  so  that  seen  in  one  of  these  mirrors, 
all  the  parts  of  the  object  shall  appear  in  their 
true  proportions.     Thus,  let  A,  figure  169,  be  a 
cylindrical  mirror,  standing  perpendicularly  upon 
the  paper,  and  let  the  figure,  B  C  D  E,  be  observed 
as  it  will  be  reflected  from  its  surface.     It  will 
then  appear  as  a  perfect  square,  F,  the  distortion 
in  the  picture  being  necessary  to  give  it  this  form 
after  reflection  from  a  cylindrical  surface. 

Fig.  169. 

Quest.  358.  May  mirrors  of  other  forms,  besides  those  already  described, 
be  constructed  ?  What  is  said  of  the  images  formed  by  them  ?  How  may 
the  effect  of  a  cylindrical  mirror  be  familiarly  shown  ?  When  will  the  parts 
of  the  face  be  diminished  in  length,  and  when  in  breadth  ?  359.  What  must 
be  the  form  of  a  figure  that  will  produce  a  square  when  viewed  in  a  cylindri- 
cal mirror  ?  What  are  these  changes  of  form  sometimes  called  ? 


OPTICS 


183 


Figure  170  represents  a  cylin- 
drical mirror,  A  B,  with  a  dis- 
torted figure,  MN,  in  front  of  it, 
the  image  of  which  in  the  mirror 
assumes  the  appearance  of  a  re- 
gular portrait. 

The  changes  of  form  prod  uced 
in  this  way  are  sometimes  called 
anamorphoses. 


Fig.  170. 

REFRACTION    OF    LIGHT. 

360.  We  have  heretofore  seen  that  a  ray  of  light  usually 
moves  in  a  straight  line ;  but  this  is  the  case  only  while  it  is 
passing  in  the  same  uniform  medium,  as  through  the  air ;  when 
it  passes  obliquely  from  one  medium  to  another,  as  from  air  to 
water  or  glass,  or  from  either  of  these  into  the  air,  it  is  bent 
more  or  less  out  of  a  straight  line,  and  is  said  to  be  refracted. 
But  if  the  ray  passes  perpendicularly  from  one  medium  to  the 
other,  it  is  not  then  refracted. 

Let  MN  and  PQ,,  figure  171,  be 
two  media,  lying  in  contact  with 
each  other,  the  lower  of  which  is 
most  dense,  and  two  rays,  as  A  B 
and  C  B,  passing  through  them. 
A  B,  being  perpendicular  to  the 
surfaces  of  the  media,  will  not  be 
bent  out  of  its  course,  but  will 
proceed  in  a  straight  line  to  E; 
but  the  ray,  C  B,  on  arriving  at  B, 
instead  of  continuing  a  straight 
course  to  D,  will  be  bent  downward,  and  take  the  direction 
B  F ;  that  is,  it  will  be  bent  or  refracted  towards  the  perpendi- 
cular, B  E.  On  the  other  hand,  when  a  ray  passes  obliquely 
from  a  dense  to  a  rare  medium,  it  will  be  refracted  from  the 
perpendicular.  Let  the  ray  be  supposed  to  pass  from  F  to  B, 
when  it  arrives  at  B,  it  will  be  bent  downward  from  the  per- 
pendicular BA,  and  take  the  direction  BC.  When  the  ray 

Quest.  360.  What  will  be  the  effect  when  a  ray  of  light  passes  obliquely 
from  one  medium  to  another  of  different  density  ?  Will  the  ray  be  refracted 
when  it  passes  perpendicularly  from  one  medium  to  the  other  ?  When  the 
r  ty  passes  from  a  rare  to  a  denser  medium,  in  what  direction  is  it  refracted  ? 


184  NATURAL     PHILOSOPHY. 

passes  from  the  rare  medium,  M  N,  to  the  denser  medium,  P  Q, 
the  angle,  A  B  C,  is  called  the  angle  of  incidence,  and  FEE 
the  angle  of  refraction;  but,  if  it  passes  in  the  opposite  direc- 
tion, then  FEE  is  the  angle  of  incidence,  and  ABC  the  angle 
of  refraction. 

The  refraction  of  light  may  be  well 
illustrated  by  a  well-known  simple  expe- 
riment. Place  a  piece  of  money,  E,  figure 
172,  in  an  empty  basin,  and  stand  by  the 
side  of  it,  having  the  eye  at  A,  just  so  that 
the  money  may  be  concealed  by  the  side 
of  the  vessel.  Then  let  an  attendant  pour 
in  water,  and  the  money  will  be  seen  gra- 
.  ITS.  dually  to  come  into  view,  and  to  appear 

as  if  situated  at  B'  instead  of  B.  The  ray  of  light  from  B,  after 
the  vessel  is  filled  with  water,  in  passing  from  the  dense  me- 
dium, water,  to  the  air,  which  is  much  less  dense,  instead  of 
passing  directly  to  C,  as  it  did  before  the  water  was  poured  in, 
is  now  bent  downward,  and  proceeds  to  the  eye  at  A.  But,  as 
an  object  always  appears  to  be  situated  in  the  direction  of  the 
ray  when  reaching  the  eye,  the  piece  of  money  will  now  appear 
to  be  at  B',  as  stated  above. 

It  is  in  consequence  of  refraction  that  a  spoon  in  a  tumbler 
of  water  always  appears  bent  at  the  surface;  the  rays  of  light 
from  the  part  above  the  water  come  directly  to  the  eye,  but 
those  from  the  part  beneath  the  water,  being  bent  downward 
as  they  enter  the  air,  cause  that  part  of  it  to  appear  elevated 
above  its  true  position  ;  and  of  course  it  will  seem  to  be  bent 
just  at  the  surface. 

361.  All  substances  do  not  refract  light  equally,  some  possess- 
ing the  power  of  bending  it  much  more  out  of  its  original  course 
than  others ;  but  it  is  always  to  be  remembered  that  in  any  par- 
ticular case  the  amount  by  which  the  ray  will  be  bent  out  of  its 
course  will  depend  upon  the  nature  of  the  medium  it  leaves,  as 
well  as  upon  that  of  the  medium  it  enters.  Thus,  a  ray  passing 
from  air  into  glass,  is  more  bent  out  of  its  course  than  when 
passing  from  water  to  glass ;  so  when  the  ray  passes  from  glass 
to  air,  it  is  bent  more  from  a  straight  line  than  when  passing 
from  glass  to  water.  As  air  is  always  present,  when  the  re- 
fracting power  of  a  substance  is  spoken  of,  if  nothing  is  said  to 
the  contrary,  the  light  is  supposed  to  pass  from  air  into  it,  or 
the  reverse. 


In  what  direction  is  the  ray  refracted  when  it  passes  from  a  dense  to  a  rare 
medium  ?  By  what  familiar  experiment  may  the  refraction  of  light  be  illus- 
trated ?  Why  does  the  object  become  visible  as  the  water  is  poured  in  ? 
Why  does  a  spoon  in  a  tumbler  of  water  appear  broken  at  the  surface  ? 
361.  Do  all  bodies  refract  light  equally  ?  Will  a  ray  of  light  be  most  bent 
out  of  its  original  course  in  passing  from  air  to  glass,  or  from  water  to  glass  ? 


OPTICS 


185 


362.  Light  is  often  irregularly  refracted  by  passing  through 
a  medium,  the  density  of  which  is  not  uniform.   It  is  the  change 
of  density  that  often  causes  the  appearance  of  veins  and  irre- 
gularities in  glass  and  other  transparent  substances. 

Every  one  has  noticed  the  peculiar  wave-like  motion  that 
seems  to  be  going  on  in  the  air  by  the  side  of  a  hot  stove  or 
stove-pipe ;  it  is  best  seen  by  attempting  to  look  directly  by  the 
stove  to  some  object,  as  a  window,  beyond  it.  This  is  occa- 
sioned by  the  unequal  refracting  powers  of  different  portions 
of  the  air,  as  they  are  expanded  unequally,  and  put  in  motion 
by  the  heat.  The  rays  of  light,  in  passing  through  air  in  this 
state,  are  indeed  but  slightly  bent  out  of  their  direct  course, 
but  it  is  distinctly  perceptible  to  the  eye. 

The  same  appearance  is  sometimes,  though  rarely,  observed 
in  the  open  air,  in  peculiar  states  of  the  atmosphere,  in  the  warm 
weather  of  summer. 

363.  When  light  traverses  a  medium,  the  density  of  which 
varies  uniformly,  it  describes  a  curve.     This  is  the  case  with 
the  light  of  the  heavenly  bodies  in  passing  through  the  earth's 
atmosphere,  so  that  we  never  see  them  in  their  true  places, 
except  when  they  are  directly  over  our  heads. 

Thus,  let  S,  figure  173,  be 
the  sun  in  the  horizon,  and  E,  a 
_/"';=  section  of  the  earth  with  the 
gf  atmosphere  surrounding  it.  As 
the  atmosphere  is  much  more 
dense  near  the  earth  than  at  a 
distance  from  it  (§  217),  a  ray 
of  light  from  the  sun  in  or  near 
the  horizon,  after  entering  it, 
as  at  A,  will  gradually  be  bent 
downward  as  it  approaches  the  earth.  A  spectator  at  B, 
therefore,  instead  of  seeing  the  sun  at  S,  its  true  place,  will 
see  it  considerably  higher,  as  at  S'.  It  is  found  that  in  conse- 
quence of  the  sun's  apparent  elevation  from  this  cause,  he  ac- 
tually appears  above  the  horizon  at  rising  about  three  minutes 
earlier,  and,  at  setting,  remains  the  same  time  longer,  than  he 
otherwise  would,  thus  increasing  the  length  of  the  day  about 
six  minutes. 

Quest.  362.  How  is  light  affected  in  passing  through  a  medium  of  varying 
density  ?  How  is  the  wave-like  motion,  often  seen  in  the  air  by  the  side  of  a 
heated  stove,  accounted  for?  Is  the  same  appearance  sometimes  observed 
in  the  open  air  ?  363.  What  is  the  course  of  a  ray  of  light  in  passing  through 
a  medium,  the  density  of  which  varies  uniformly  ?  How  is  the  light  of  the 
sun  affected  by  the  earth's  atmosphere  ?  Do  we  ever  see  the  heavenly  bo- 
dies in  their  true  places  ?  Do  we  see  the  heavenly  bodies  when  near  the 
horizon  above  or  below  their  true  places  ?  How  much  longer  does  the  sun 
appear  above  the  horizon  at  setting,  in  consequence  of  refraction,  than  he 
otherwise  would  ? 

16* 


Fig.  ]73. 


186  NATURAL     PHILOSOPHY. 

364.  Bodies  seen  in  the  horizon  in  peculiar  states  of  the  at- 
mosphere, sometimes  appear  singularly  elevated  by  this  cause 
above  their  proper  natural  position,  and  are  said  by  sailors  to 
loom  up.     A  ship  at  a  distance,  or  an  island  with  the  buildings 
upon  it,  will  perhaps  appear  twice  their  ordinary  height  above 
the  surface  of  the  sea,  while  their  other  dimensions  remain  as 
usual.     This  is  occasioned  by  the  unusually  great  refracting 
power  of  the  atmosphere,  by  reason  of  the  temperature  and  the 
presence  of  other  substances,  as  vapors,  floating  in  it.     The 
writer  has  often  observed  this  appearance  in  a  striking  manner 
on  the  coast  of  New  England,  just  before  the  commencement 
of  severe  snow-storms. 

365.  Total  Reflection  of  Light.  —  A  ray  of  light  cannot  pass 
from  a  dense  to  a  rare  medium,  but  is  totally  reflected,  when- 
ever the  angle  of  incidence  exceeds  a  certain  magnitude,  de- 
pending upon  the  nature  of  the  medium. 

Let  ABC,  figure  174,  be  a  section  of 
a  prism  of  glass,  and  R  a  ray  of  light 
entering  it  perpendicularly  and  incident 
upon  the  inner  surface,  B  C,  at  D  ;  if  the 
angle  of  incidence,  P  D  R,  is  greater  than 
41°  48',  none  of  the  light  will  pass  out 
at  D,  but  the  whole  will  be  reflected 
upward  to  R'.  It  is,  therefore,  properly 
said  to  be  totally  reflected.  If  the  angle, 
P  D  R,  is  a  little  less  than  41°  48',  a  por- 
tion of  the  light  will  pass  out  at  D,  and  take  the  direction 
DR". 

The  brilliancy  of  light,  when  totally  reflected,  far  exceeds 
that  reflected  from  the  most  perfect  mirrors.  To  show  this,  let 
a  tumbler  nearly  filled  with  clear  water,  be  held  up  so  that  the 
upper  surface  of  the  liquid  may  be  seen  from  beneath  ;  it  will 
appear  of  a  beautiful  silvery  whiteness,  by  reason  of  the  total 
reflection  of  the  light  incident  upon  it,  and  no  object  held  above 
it  will  be  visible  through  it. 

366.  Progress  of  Light  through  different  Media.  —  The  pro- 
gress of  a  ray  of  light  through  any  medium  of  uniform  density- 
may  always  be  easily  traced  by  means  of  the  foregoing  princi- 
ples, and  the  result  determined. 

In  passing  through  a  pane  of  glass,  or  any  medium  bounded 

Quest.  364.  When  are  distant  bodies  said  by  sailors  to  loom  up  ?  How  is 
this  appearance  occasioned  ?  Under  what  circumstances  is  this  phenomenon 
often  seen  on  the  coast  of  New  England  ?  365.  What  is  meant  by  the  total 
reflection  of  light  ?  What  is  the  greatest  angle  of  incidence  a  rav  of  light 
can  have  in  passing  from  glass  into  the  air  ?  What  will  be  the  effect  if  the 
ancrle  of  incidence  is  greater  than  41°  48  ?  What  is  said  of  the  brilliancy  of 
light  when  totally  reflected  ?  How  may  this  be  shown  by  moans  of  a  tum- 
bler of  clear  water  ?  366.  Will  the  foregoing  principles  be  sufficient  to  deter- 
mine the  course  of  a  ray  in  passing  from  one  medium  to  another  ?  Is  the 
direction  of  a  ray  changed  in  passing  a  pane  of  glass  which  has  its  two  plane 


OPTICS.  187 

by  two  parallel  plane  surfaces,  the  direction  of  a  ray  of  light  is 
not  changed,  but  its  position  is  more  or  less  altered. 

Thus,  let  AB,  figure  175,  be  a  piece  of 
plate  glass,  the  surfaces  of  which  are  per- 
fectly parallel,  and  let  C  D  be  a  ray  of  light 
incident  at  D ;  it  will,  on  entering  and  leav- 
ing the  glass,  be  refracted,  according  to  the 
laws  already  stated  (§  360) ;  but  both  refrac- 
tions will  be  exactly  equal  in  amount,  and 
in  opposite  directions ;  that  is,  it  will  be  bent 
upward  at  D,  and  downward  by  an  equal 
amount  at  K ;  so  that  K  E  will  be  parallel  to 
CD.  It  is,  however,  moved  a  little  to  one 
Fig.  175.  s^e  from  its  former  position,  by  the  distance, 

in  the  present  case,  between  K  E  and  the  dotted  line  extending 
fro-m  D.  This  distance  must  always  be  less  than  the  thickness 
of  the  glass.  The  effect  of  this  upon  converging  rays  is  to  pre- 
vent their  coming  to  a  focus  as  soon  as  they  otherwise  would. 
Let  F  G  H  be  several  converging  rays;  it  will  be  seen  by  tracing 
their  course,  that  after  emerging  from  the  glass,  they  are  re- 
moved a  little  farther  from  each  other  than  they  were  before, 
and  must  proceed  a  little  farther  before  meeting.  Diverging 
rays  are,  in  the  same  manner,  brought  a  little  nearer  toge- 
ther. 

367.  If  the  two  surfaces  of  the  glass  where  the  light  enters 
and  leaves  it  are  not  parallel,  the  ray  will  be  bent  more  or  less 
out  of  its  course. 

Let  ABC,  figure  176,  be  the 
section  of  a  triangular  prism,  of 
which  AC  and  CB  are  the  re- 
fracting surfaces,  and  A  B  the 
base.  A  ray  of  light,  D  E,  from  a 
luminous  body,  D,  on  entering 
the  glass,  will  be  bent  downward 
in  the  direction  E  F ;  and  again, 
on  escaping  into  the  air,  it  will  be 

bent  downward  in  the  direction  FG;  so  that  both  refractions 
turn  it  from  its  original  course  in  the  same  direction.  If  an 
eye  is  situated  at  G,  the  object,  D,  will  appear  to  be  at  d,  in  the 
direction  ofGF  produced. 

368.  Instead  of  a  solid  glass  prism,  as  represented  above,  one 

surfaces  parallel  ?  Will  the  refraction  of  the  ray,  as  it  leaves  the  glass,  be 
just  equal  to  that  which  took  place  as  it  entered  ?  Will  converging  rays 
come  to  a  focus  as  soon  after  passing  through  a  glass  of  this  kind  as  they 
otherwise  would  ?  What  will  be  the  effect  upon  diverging  rays  ?  367.  If 
the  two  surfaces  are  not  parallel,  what  will  be  the  effect  ?  What  is  shown 
in  figure  176  ?  Where  will  the  object  appear  to  be  situated  to  an  eye  at  G  ? 
368.  Is  a  solid  glass  prism  necessary  for  this  experiment  ?  How  may  a 


188  NATURAL     PHILOSOPHY. 

may  easily  be  formed  for  the  purpose,  by  having  a  frame  made 
of  tin,  or  even  of  wood,  and  puttying  in  three  pieces  of  glass, 
and  filling  it  with  water  or  other  transparent  liquid.  Or  it  will 
answer  for  many  experiments  if  made  with  only  two  sides, 
with  the  space  between  them  filled  with  water. 

Other  effects  produced  by  the  prism  upon  light  are  to  be  no- 
ticed hereafter. 

369.  Instruments  used  for  forming 
images  by  the  refraction  of  light  are 
called  lenses.  They  are  usual!)7  made 
-g — m —        — -ST  of  glass,  or  other  transparent  mine- 
ra^  substances,  and  are  of  various 
Fig.  177.  forms,  as  shown  in  figure  177. 

The  double  convex  lens,  A,  is  a  solid,  bounded  by  two  convex 
surfaces. 

The  plano-convex  Jens,  B,  is  merely  half  a  double  convex, 
one  surface  being  convex,  as  in  the  double  convex  lens,  but 
the  other  plai.e. 

The  double-concave  lens,  C,  has  both  its  surfaces  concave, 
like  a  solid  formed  of  two  watch-glasses  placed  back  to  back, 
and  the  space  between  them  filled  up  with  transparent  matter. 

The  plano-concave  lens,  D,  has  one  of  its  surfaces  concave 
and  the  other  plane. 

The  meniscus,  E,  is  a  lens  having  one  surface  convex  and  the 
other  concave,  and  these  curves  meet  if  produced.  The  con- 
vexity of  one  surface  exceeds  the  concavity  of  the.  other. 

The  concavo-convex  lens,  F,  like  the  meniscus,  has  one  sur- 
face convex  and  the  other'concave,  but  if  produced,  the  curves 
do  not  meet.  The  concavity  of  one  surface  exceeds  the  con- 
vexity of  the  other. 

In  all  these  lenses,  a  line,  M  N,  passing  through  their  centres 
and  perpendicular  to  their  surfaces  at  this  point,  is  called  the 
axis. 

370.  The  course  of  a  ray 
through  any  one  of  the  above 
lenses  may  be  easily  traced  in 
the  following  manner.  Let 
A  B  C  D,  figure  178,  be  a  spheri- 
cal lens,  which  is  only  a  parti- 
cular form  of  the  double-convex, 
and  M  N  O  be  three  parallel  rays 
incident  upon  it.  The  middle 

prism  be  fitted  for  the  purpose  ?  369:  What  are  lenseg  ?  What  are  they 
usually  made  of?  What  is  the  form  of  the  double-convex  lens  ?  What  is 
the  plano-convex  lens  ?  What  is  the  form  of  the  double-concave  lens  ?  The 
plano-concave  ?  What  is  the  form  of  the  two  surfaces  of  the  meniscus  ?  In 
what  does  the  concavo-convex  lens  differ  from  the  meniscus  ?  What  is  the 
axis  of  a  lens  ?  370.  Why  will  not  the  middle  ray,  N,  figure  178,  be  re- 


OPTICS.  189 

ray,  N,  being  perpendicular  to  the  surface,  will  not  be  refracted 
in  passing  through  the  lens;  but  the  rays,  M  and  O,  on  entering 
the  lens  at  A  and  D  (being  refracted  towards  the  perpendicu- 
lars, A  S  and  D  S),  will  be  made  slightly  to  converge ;  and,  on 
leaving  the  lens,  (being  refracted  from  perpendiculars  at  the 
points  B  C,  will  be  made  to  converge  still  more ;  and  the  result 
will  be  to  bring  them  to  a  focus  at  P. 

The  effect  of  the  double-convex  lens  is  precisely  the  same  as 
that  of  the  sphere,  but  somewhat  less  in  degree.  It  is  to  collect 
the  rays. 

371.  The  distance  of  the  focus  of  parallel  rays  from  the  con- 
vex lens  depends  upon  the  degree  of  convexity.    In  the  double- 
convex  lens  of  glass,  it  is  at  the  distance  of  the  centre  of  the 
sphere  of  which  the  lens  is  a  part;  but,  in  the  plano-convex 
lens,  the  focus  is  at  the  distance  of  the  diameter  of  the  sphere, 
or  twice  the  radius. 

Let  A  B,  figure  179,  be  a  double  con- 
vex lens,  having  each  of  its  faces  a 
portion  of  the  surface  of  a  sphere  whose 
centre  is  at  C,  then  this  will  be  the 
point  to  which  parallel  rays,  M,  will  be 
made  to  converge.    If  one  side  was 
plane,  then  parallel  rays  would  con- 
Fig.  179.  verge  to  the  point,  D,  at  the  distance 
of  the  diameter  of  the  same  sphere. 

372.  If  the  rays  are  converging  before  entering  the  double 
convex  lens,  the  focus  will  be  nearer  the  lens  than  the  centre 
C,  but  if  they  are  diverging,  it  will  be  farther  from  the  lens. 
The  same  effect  will  also  be  produced  upon  the  focal  distance 
of  the  plano-convex  lens. 

The  well-known  burning-glass  is  usually  a  double-convex 
lens ;  and  its  effect,  when  held  in  the  direct  rays  of  the  sun, 
is  simply  to  concentrate  the  rays  of  heat,  as  well  as  those  of 
light,  to  a  point  or  focus.  And  the  heat  at  this  point  is  as  much 
greater  than  the  heat  of  the  sun  at  the  glass,  as  the  surface 
over  which  it  is  distributed  is  less. 

Burning-glasses  of  great  power  have  sometimes  been  con- 

fracted  in  passing  the  spherical  lens  ?  In  what  direction  will  the  rays,  M  and 
O,  be  refracted  on  entering  the  lens  and  on  leaving  it  ?  What  will  the  result 
be  ?  Is  the  effect  of  the  double -convex  lens  the  same  ?  Upon  what  does  the 
distance  of  the  focus  from  the  lens  depend  ?  What  is  the  distance  of  the 
focus  of  a  double-convex  lens  ?  What  is  the  distance  in  a  plano-convex  lens  ? 
372.  If  the  rays  are  converging  before  entering  the  lens  will  the  distance  of 
the  focus  be  greater  or  less  than  if  they  were  parallel  ?  What  is  the  common 
burning-glass  ?  What  is  its  effect  when  held  in  the  direct  rays  of  the  sun  ? 
How  much  greater  is  the  heat  in  its  focus  than  the  heat  of  the  sun  before 
being  concentrated  ?  What  was  the  diameter  of  Mr.  Parker's  great  burning- 
glass  ?  Why  was  a  second  lens  used  with  it  ?  What  is  said  of  the  heat 
capable  of  being  produced  by  such  an  instrument  ? 


190  NATURAL     PHILOSOPHY. 

structed.  One  made  by  Mr.  Parker  was  three  feet  in  diameter, 
and  had  a  second  smaller  lens  connected  with  it  in  order  to 
diminish  the  diameter  of  the  focus.  The  heat  of  the  sun  when 
concentrated  by  it  was  so  great  as  to  be  capable  of  melting 
the  less  fusible  metals,  as  gold  and  platinum,  and  other  refrac- 
tory substances.  Indeed,  such  an  instrument  is  perhaps  capa- 
ble of  producing  as  great  a  heat  as  can  be  produced  by  man 
by  any  other  means. 

373.  The  effect  of  the  double- con- 
cave lens  is  to  disperse  the  rays  of 
light.  Let  A  B,  figure  180,  be  a  dou- 
ble-concave lens,  having  both  its  sur- 
faces portions  of  equal  spheres ;  and 
suppose  parallel  rays,  M,  to  be  inci- 
dent upon  it  in  the  manner  shown. 
Fig.  iso.  These  rays  will  be  made  to  diverge 

by  passing  through  the  lens,  and  to  appear  to  proceed  from'a 
point,  as  C,  which  is  therefore  called  the  virtual  or  apparent 
focus. 

The  effect  of  the  plano-concave  lens,  it  is  easy  to  see,  will  be 
the  same  as  that  of  the  double-concave,  but  only  less  in  de- 
gree. 

The  effect  on  converging  rays  by  either  of  these  lenses  will 
depend  upon  the  degree  of  their  converging;  if  they  are  very 
converging,  they  may  still  converge  after  passing  the  lens,  but 
in  less  degree ;  but,  if  their  convergency  is  not  great,  they  will 
either  be  parallel,  or  be  made  to  diverge  after  passing  it. 
Diverging  rays  will  be  made  still  more  diverging. 
The  action  of  the  meniscus  is  the  same  as  that  of  a  double- 
convex  lens  of  the  same  focal  distance,  the  effect  of  the 
convex  side  in  converging  the  rays  being  greater  than  that  of 
the  concave  side  in  separating  them.  So  the  effect  of  the 
concavo-convex  lens  is  the  same  as  that  of  the  double-concave 
lens. 

374.  Formation  of  Images  by  Lenses. — Images  are  formed  by 
lenses  much  in  the  same  manner  in  several  respects  as  they 
are  by  mirrors.  As  we  have  before  seen  (§  351),  rays  of  light 
are  emitted  from  every  point  of  a  visible  object;  and  when  the 
object  is  so  arranged  with  reference  to  a  convex  lens  that  a 
portion  of  these  rays  from  each  point  are  again  united  in  re- 
guJar  order,  an  image  of  it  will  be  formed. 

Quest.  373.  What  is  the  effect  of  the  concave  lens  upon  rays  of  light  ? 
What  is  its  virtual  or  apparent  focus  ?  What  will  be  the  effect  of  a  concave 
lens  upon  converging  rays  ?  How  will  diverging  rays  be  affected  ?  What 
is  said  of  the  action  of  the  meniscus  ?  374.  When  will  an  image  of  an  object 
be  produced  by  a  convex  lens  ?  May  we  consider  the  images  of  all  the 
points  of  the  object  to  be  formed  separately  ?  What  will  be  the  position  of 
the  image  in  reference  to  the  object  ? 


7/x 


OPTICS.  191 

Let  L  C  L,  figure  181, 
be  a  double  convex  lens, 
and  MN  an  object  in 
front  of  it.  From  every 
point,  as  M,  rays  are 
emitted  in  every  direc- 
tion ;  but  a  cone  of  them 
represented  by  M  L  L, 
is  intercepted  by  the 
^  ]S  lens'  and  again  united 
Fig.  isi.  at  m,  forming  there  an 

image  of  the  point  M. 

In  the  same  manner,  by  a  cone  of  rays  emitted  from  N,  an 
image  .of  this  point  will  also  be  produced  at  n;  and  thus  an 
image  of  all  the  points  of  M  N  will  be  formed  in  mn,  in  their 
proper  order,  though  in  an  inverted  position,  in  reference  to 
the  object. 

375.  The  size  of  the  image,  as  compared  with  the  object,  will 
depend  entirely  upon  its  distance  from  the  lens,  compared  with 
the  distance  of  the  object.  If  the  object  is  at  a  great  distance, 
the  image  will  be  near,  and  will  be  much  smaller  than  the 
object ;  but  if  the  object  is  near  the  lens,  the  image  will  be 
formed  at  a  distance,  and  will  be  larger  and  less  distinct  than 
before. 

An  easy  experiment  illustrating  these  points  may  be  readily 
performed  in  the  evening,  or  in  a  darkened  room,  by  means 
of  a  candle  and  a  common  magnifying-glass,  or  one  lens  of 
spectacles  used  by  an  aged  person. 

Suppose  A  B,  figure  182,  to  be 
a  glass  of  this  kind,  and  CD  the 
flame  of  a  candle  placed  at  a  consi- 
derable distance  from  it.  As  be- 
fore explained,  a  diminished  and 
inverted  image  of  the  flame  will 
be  formed  on  a  piece  of  white  pa- 
per held  at  C'D'.  If,  now,  we 
place  the  candle  at  C'  D',  and  the  paper  at  C  D,  an  inverted  but 
enlarged  image  of  the  candle  will  be  formed  upon  it.  It  is  to 
be  observed  that,  whatever  may  be  the  diameter  of  the  lens,  it 
does  not  affect  the  magnitude  of  the  image ;  this  depends  en- 
tirely upon  its  convexity.  Two  lenses,  therefore,  of  the  same 
convexity,  will  form  images  of  the  same  size,  though  one  lens 
may  be  larger  than  the  other;  but  the  image  of  the  larger  lens 

Quest.  375.  Upon  what  will  the  size  of  the  image,  as  compared  with  the 
object,  depend  ?  When  will  the  image  be  smaller  than  the  object  ?  and  when 
larger  ?  How  may  experiments  illustrating  these  principles  be  readily  per- 
formed ?  Will  the  magnitude  of  the  image  depend  in  any  degree  upon  the 
diameter  of  the  lens  ?  Will  two  lenses  of  the  same  convexity  form  images 
of  the  same  magnitude,  whatever  may  be  their  comparative  diameters  ?  Why 


Fig.  182. 


192  NATURAL     PHILOSOPHY. 

will  be  brightest,  because  of  the  greater  number  of  rays  from 
the  object  intercepted  by  it. 

The  effect  of  the  concave  lens  being  to  disperse  the  rays  of 
light,  it  is  evident  no  image  can  be  formed  by  it> 

376.  The  formation  of  images  by  spherical  lenses  is  attended 
by  a  practical  difficulty  which  it  has  not  yet  been  found  possi- 
ble entirely  to  avoid,  called  spherical  aberration.     Let 

A  B,  figure  183,  be  a  very  convex 
lens,  and  let  C  D  E  F  G  be  parallel  rays, 
the  central  one  of  which,  E,  being  in 
the  axis  of  the  lens,  will  pass  perpendi- 
cularly through  it,  without  refraction. 
But  the  other  four  rays,  being  inclined 
to  the  surface  of  the  glass,  will  be  more 
or  less  refracted  in  passing  through  it, 
and,  as  before  explained  (§  370),  will  be  brought  to  a  focus. 
But  it  will  be  seen,  by  a  little  examination  of  the  figure,  that 
the  rays  I^and  F  nearest  the  axis  are  less  inclined  to  the  sur- 
face of  the  glass  as  they  enter  it  than  the  exterior  rays  C  and 
G;  they  will  therefore  be  less  refracted,  and  will  form  their 
focus  farther  from  the  glass  than  the  exterior  rays.  The  focus 
of  the  former  rays  will  be  at  n,  while  that  of  the  latter  will  be 
at  m,  wrTere  they  will  cross  each  other. 

-  Now,  if  with  such  a  glass  we  attempt  to  form  an  image  of 
any  object,  the  result  of  course  is,  that  instead  of  a  single"  well- 
defined  image,  the  tendency  is  to  produce  several  images  at 
different  points  which  will  confuse,  and,  in  a  measure,  destroy 
each  other.  This  defect  may,  to  some  extent,  be  remedied  in 
large  lenses  by  covering  all  the  lens  except  a  small  part  at  the 
centre,  and  thus  excluding  all  the  rays  except  the  central  ones, 
but  this  greatly  diminishes  the  quantity  of  light.  By  means  of 
the  meniscus,  and  also  by  different  combinations  of  plano- 
convex lenses,  the  difficulty  may  be  in  a  great  measure  avoid- 
ed, but  no  means  have  yet  been  devised  by  which,  in  the  use 
of  spherical  lenses,  it  can  be  completely  dispensed  with. 

377.  To  remedy  this  evil  it  has  been  proposed  to  construct 
lenses  of  other  forms  than  the  spherical ;  but  the  mechanical 
operations  required  in  grinding  and  polishing  them  are  so  diffi- 
cult that  the  project  has  been  relinquished. 

will  the  image  formed  by  the  larger  lens  be  brightest  ?  Can  images  be  pro- 
duced by  the  concave  lens  ?  376,  What  practical  difficulty  attends  the  for- 
mation of  images  by  spherical  lenses  ?  When  parallel  rays  pass  through  a 
convex  lens,  will  all  of  them  meet  in  the  same  focus  ?  Are  the  rays  near  the 
axis  of  the  lens  or  those  farther  from  it  brought  to  a  focus  nearest  the  lens  ? 
Will  a  single  image  be  formed  by  such  a  lens  ?  How  may  this  effect  be  to 
some  extent  remedied  ?  Have  any  means  yet  been  devised  by  which  it* can 
be  completely  avoided  ?  377.  Why  has  it  been  proposed  to  construct  lenses 
of  other  forms  ?  Why  has  the  project  been  relinquished  ?  Does  spherical 
aberration  take  place  also  in  concave  mirrors  1 


. 

OPTICS.  193 

Spherical  aberration  takes  place  also  in  concave  lenses  of 
every  form. 

In  concave  mirrors,  likewise,  of  a  spherical  form,  the  same 
difficulty  is  to  be  encountered,  but  it  is  of  less  importance  than 
in  the  case  of  lenses. 

SEPARATION  OF  THE  DIFFERENTLY  COLOURED  RATS. 
COLOURS  OF  BODIES. 

378.  White  light,  as  it  is  emitted  from  the  sun  or  other  lumin- 
ous bodies,  is  composed  of  rays  of  several  different  colours, 
which  may  be  separated  from  each  other.  Newton,  who  first 
gave  his  attention  to  this  subject,  reckoned  no  less  than  seven 
colours  as  composing  white  light,  viz:  red,  orange,  yellow, 
green,  blue,  indigo,  and  violet,  which  he  called  primary  colours; 
but  the  more  recent  investigations  of  Brewster  have  rendered 
it  probable  that  the  white  ray  of  the  sun  contains  only  three 
rays,  the  red,  the  yellow,  and  the  blue.  The  other  colours  of 
Newton  are  probably  produced  by  different  combinations  of 
these  three. 

Newton's  method  of  separating  the  several  rays  was  by 
means  of  the  triangular  prism,  which  is  only  a  solid  piece  o"f 
glass,  bounded  by  three  perfectly  plane  faces  Usually  the  faces 
are  equally  inclined  to  each  other,  but  this  is  not  essential. 

Let  a  ray  of  light  from  the 
sun,  S,  figure  184,  be  ad- 
mitted through  a  hole  in  the 
'S  window-shutter,  D  E,  into  a 
room  from  which  all  other 
light  is  excluded;  it  will 
form  on  a  screen  placed  a 
little  distance  in  front  a  cir- 
cular image,  W,  of  white 
light.  Now,  interpose  near 

,.'/'  the  shutter  a  glass  prism, 

<£/'  ABC,  and  the  light,  in  pass- 

ing  through  it,  will  not  only 
be  refracted,  but  the  several 

colours  of  which  white  light  is  composed  will  be  separated,  and 
will  be  arranged  in  regular  order  on  the  screen  immediately 
above  the  image  W,  which  will  disappear.  The  violet  ray,  it 
will  be  seen,  is"  most  refracted  or  bent  out  of  its  course,  and 

Quest.  378.  What  is  white  light,  as  it  is  emitted  from  the  sun  and  other 
luminous  bodies,  composed 'of  ?  .How  many  coloured  rays  did  Newton  sup- 
pose enter  into  the  composition  of  white  light  ?  What  coloured  rays  only 
are  contained  in  white  light  according  to  Brewster  ?  How  are  the  other 
colours  of  Newton  produced  ?  What  was  Newton's  method  of  separating 
the  several  coloured  rays  ?  What  is  illustrated  in  figure  184  ?  Which  ray 

17 


194  NATURAL     PHILOSOPHY. 

the  red  least,  while  the  other  colours  are  between  them ;  the 
whole  forming  on  the  screen  an  elongated  image  of  the  sun, 
called  the  solar  spectrum. 

The  separation  of  the  several  rays  is  evidently  occasioned 
by  their  different  refrangibility,  the  glass  of  the  prism  having 
the  power  to  turn  some  farther  out  of  their  course  than  others. 
But  it  is  to  be  observed  that  these  colours  in  the  spectrum  are 
not  separated  from  each  other  by  distinct  and  well-defined 
edges,  but  each  runs  into  the  other,  the  red  shading  off  by  im- 
perceptible gradations  into  the  orange,  the  orange  into  the 
yellow,  the  yellow  into  the  green,  &c. 

Newton,  indeed,  and  others  since  his  day,  have  attempted  to 
measure  the  width  of  the  several  colours  in  the  spectrum ;  but, 
as  might  be  expected,  the  results  obtained  by  different  indivi- 
duals are  far  from  being  uniform.  And  it  is 'now  known  that 
their  apparent  width,  compared  with  the  whole  width  of  the 
spectrum,  will  greatly  depend  upon  the  particular  kind  of 
glass,  or  other  transparent  substance,  which  may  be  used. 
The  results  with  a  prism  of  flint-glass,  for  instance,  will  be 
different  from  those  obtained  when  one  of  crown-glass  is  used  ; 
so  also  if  a  prism  of  water  contained  in  a  prismatic  glass  vessel 
(5  368)  is  made  use  of,  the  results  will  be  entirely  different  from 
those  obtained  with  a  prism  of  alcohol,  or  sulphuric  acid,  or 
solution  of  salt. 

379.  It  appears,  therefore,  that  the  white  light  of  the  sun  is 
composed  of  several  differently  coloured  rays,  and  the  effect 
of  the  prism  is  merely  to  separate  them  from  each  other. 

It  matters  not  in  practice  whether,  with  Newton,  we  consider 
there  are  seven  differently  coloured  rays,  or  with  Brewster  that 
there  are  only  three,  since  the  results  will  be  the  same.  If  a 
second  prism,  AFC,  precisely  like  the  first,  be  placed  beyond 
it,  but  in  contact  with  it,  and  In  a  reversed  position,  the  several 
rays  which  are  separated  by  the  first  prism  will  be  reunited 
by  the  second,  and  beyond  it  nothing  but  the  pure  white  light 
of  the  sun  will  appear. 

The  several  coloured  rays  may  also  be  recombined  by  hold- 
ing a  convex  lens  near  the  prism  between  it  and  the  screen, 
so  as  to  bring  them  to  a  focus,  which  will  be  perfectly  white. 


is  refracted  most,  and  which  least  ?  What  is  the  solar  spectrum  ?  How  is 
the  separation  of  the  rays  occasioned  ?  Are  the  colours  of  the  spectrum 
separated  by  a  distinct  line  ?  Will  the  width  of  the  several  colours  be  the 
same  where  prisms  of  different  refracting  substances  are  used  ?  If  hollow 
prisms  filled  with  different  liquids,  as  water  and  alcohol,  are  used,  will  the 
width  of  the  colours  be  the  same  ?  379.  Is  it  important  whether  we  consider 
that  the  solar  beam  is  composed  of  seven  coloured  rays,  or  only  three  ?  How 
is  it  shown  that  the  reunion  of  the  coloured  rays  of  the  spectrum  will  produce 
white  light  ?  May  the  coloured  rays  also  be  reunited  by  a  convex  lens,  so 
as  to  produce  white  light  ? 


OPTICS.  195 

380.  The  same  point  may  be  illustrated  further  by  mixing 
powders  of  the  several  different  colours  in  the  proper  propor- 
tion, which  will  produce  a  greyish-white.  A  pure  white  cannot 
be  produced  in  consequence  of  the  impossibility  of  obtaining 
powders  of  precisely  the  proper  shade. 

If  we  take  a  circle  of  wood,  figure  185,  and  put  a 
pin  through  its  centre  for  it  to  revolve  upon  like  a 
top,  and  divide  it  into  sections  R,  O,  Y,  G,  B,  I,  and 
V,  of  the  proper  proportions,  by  pasting  upon  it 
pieces  of  paper  of  the  different  colours  of  the  spec- 
trum, when  it  is  made  to  revolve  rapidly,  the  whole 
will  appear  of  a  grayish-white  as  before.  The  violet, 
V,  is  designed  to  occupy  about.  80  degrees  of  the  cir- 
cumference; the  indigo,  I,  80°;  the  blue,  B,  60°; 
Fig.  185.  the  green,  G,  60°  ;  the  yellow,  40°  ;  the  orange,  27°  ; 

and  the  red,  45° ;  which,  according  to  Newton,  is  the  proportion  of  the 

spaces  occupied  by  these  colours  in  the  spectrum. 

381.  Whether  we  regard  the  seven  colours  of  Newton  as 
simple  or  not,  it  is  found  impossible  to  produce  any  farther  de- 
composition of  any  one  of  them  by  means  of  the  prism.     This 
is  shown  by  making  a  small  hole  in  the  screen  upon  which  the 
spectrum  is' formed,  just  sufficient  for  one  of  the  rays  to  pass 
through,  and  placing  behind  it  a  second  prism,  by  which  it  is  a 
second  time  refracted,  but  no  change  of  colour  is  produced. 

382.  On  the  undulatory  theory,  which  has  already  been  par- 
tially explained  (§  330),  these  different  colours  are  supposed  to 
be  produced,  not  by  rays  of  different  colours,  but  by  differences 
in  the  amplitude  and  rapidity  of  the  vibrations  in  the  univer- 
sally diffused  ether,  occasioned  by  passing  the  prism.   Accord- 
ing to  Sir  John  Herschell,  the  extreme  red  ray  is  produced  by 
waves,  or  undulations,  the  length  of  which  is  266  ten-mill ionths 
of  an  inch,  and  458  millions  of  millions  of  them  occur  each 
second,  while  the  length  of  the  waves  producing  the  extreme 
violet  is  only  167  ten-millionths  of  an  inch,  and  727  millions  of 
millions  take  place  in  a  second.     In  the  other  colours  of  the 
spectrum,  both  the  length  of  the  waves,  and  the  number  occur- 
ring in  a  second,  are  Intermediate  between  the  numbers  above 
given  for  the  red  and  the  violet,  the  extreme  rays  of  the  spec- 
trum. 

383.  The  solar  ray  may  also  be  decomposed  by  passing  it 

Quest.  380.  How  may  the  same  point  be  further  illustrated  by  means  of 
paints  ?     Can  a  pure  white  be  produced  in  this  way  ?     What  is  the  reason  ? 

381.  Can  any  one  of  the  seven  coloured  rays  of  the  spectrum,  according  to 
Newton,  be  decomposed  by  means  of  the  prism  ?     How  is  this  shown  ? 

382.  How  are  the  different  colours  of  the  spectrum  produced  on  the  undu- 
latory theory  ?     What  is  supposed  to  be  the  extent  of  the  waves  producing 
the  extreme  red  ray  of  the  spectrum?     How  many  of  them  occur  in  a  se- 
cond ?     What  is  the  length  of  the  waves  which  produce  the  extreme  violet, 
and  how  many  occur  in  a  second  I    383,  By  what  other  means  may  the  solar 


196  NATURAL     PHILOSOPHY. 

through  some  medium  that  is  capable  of  absorbing  some  of  the 
rays  and  transmitting  others.  If,  for  instance,  a  beam  of  white 
light  be  passed  through  a  clear  blue  glass,  it  emerges  of  a  fine 
blue  colour,  having  lost  in  the  glass  the  rays  which,  when 
mixed  with  it,  produced  the  white  light.  To  determine  what 
rays  these  are,  it  is  necessary  only  to  look  at  the  solar  spectrum 
through  the  glass;  the  red  and  the  orange  will  then  disappear, 
while  the  yellow  will  be  greatly  increased  in  width,  occupying 
a  portion  of  the  space  before  covered  by  the  orange  on  one 
side,  and  the  green  on  the  other.  It  appears,  therefore,  that 
the  glass  absorbed  the  red  rays  which,  when  mixed  with  the 
yellow,  constitute  the  orange,  and  also  the  blue,  which,  with 
the  yellow,  constitute  green. 

By  experimenting  in  this  way  with  differently  coloured  media, 
it  is  found  that  there  are  in  reality  only  three  coloured  rays  in 
the  solar  spectrum,  the  red,  the  yellow,  and  the  blue,  and  that 
certain  mixtures  of  these  produce  the  other  colours.  The  solar 
spectrum  may  be  considered  as  made  up  of  three  other  spectra, 
one  of  red,  one  of  yellow,  and  one  of  blue,  which  overlap  each 
other.  Each  colour  extends  over  the  whole  of  the  spectrum, 
but  is  much  more  intense  in  that  part  where  that  colour  predo- 
minates. The  red  is  most  intense  in  the  middle  of  the  red 
space,  the  yellow  in  the  middle  of  the  yellow  space,  and  the 
blue  between  the  blue  space  and  the  indigo. 

Y  Let  C  H,  figure  186,  repre- 

/s~*\  sent  the  solar  spectrum,  the 

letters  r,  o,  y,  g,  6,  i,  v,  indi^ 
eating  the  place  of  the  seve- 
ral  colours  of  the  spectrum, 
C    r     0      y    g     &     t      v IH  red,  orange,  yellow,  green, 

1 ' ' ' ' ' ' '     &c.     We  may  suppose  the 

curves  R,  Y,  and  B,  to  indi- 
cate the  relative  intensities  of  the  three  supposed  primary  co- 
lours, red,  yellow,  and  blue,  and  also  the  parts  of  the  spectrum 
where  each  is  most  intense.  Thus,  the  red,  R,  commences  at 
C,  and  at  once  attains  its  greatest  intensity,  and  then  diminishes 
becoming  very  faint  towards  H.  The  yellow,  Y,  likewise  be- 
gins at  C,  but  does  not  so  soon  attain  its  medium  intensity, 
and  extends  farther  towards  H,  while  the  blue,  B,  commences 
very  faint  at  C,  and  becomes  most  intense  near  the  other  ex- 
tremity of  the  spectrum,  H.  Neither  the  red  nor  the  blue  is  as 

ray  be  decomposed  ?  If  we  look  at  the  solar  spectrum  through  a  blue  glass, 
what  colours  will  disappear,  and  what  colours  will  be  increased  in  width  ? 
What  is  the  occasion  of  this?  By  experimenting  in  this  manner  with  glasses 
of  other  colours,  what  rays  only,  are  we  led  to  conclude,  are  contained  in  the 
eolar  spectrum  ?  How  are  the  other  colours  produced  ?  Does  each  of  these 
coloured  rays  extend  over  the  whole  spectrum  ?  Where  is  the  red  most  in- 
tense \  Where  the  yellow  ?  How  is  this  illustrated  in  figure  186  ?  What  is 


OPTICS,  197 

intense  as  the  yellow,  as  is  designed  to  be  indicated  by  the 
curve  Y  rising  higher  than  the  others. 

Each  of  the  other  colours,  it  will  be  seen,  is  composed  chiefly 
of  two  of  the  primary  colours,  with  a  little  of  the  third.  Thus, 
the  orange  is  made  up  of  the  red  and  yellow,  with  a  very  little 
of  the  blue,  and  the  green  is  composed  of  a  mixture  of  the 
yellow  and  blue,  with  a  little  red. 

384.  The  green,  because  of  its  position  in  the  spectrum,  is 
sometimes  called  the  tnedium  or  mean  ray;  but,  though  this 
colour  is  usually  near  the  middle  of  the  spectrum,  it  is  found 
that  the  distance  the  extremes  will  be  removed  from  it  will  de- 
pend upon  the  nature  of  the  prism.     A  prism  of  hollow  glass, 
filled  with  oil  of  cassia,  for  instance,  will  form  a  spectrum  twice 
as  long,  as  one  made  of  solid  flint  glass;  and  of  course  the  two 
extremes  will  be  removed  at  twice  the  distance  from  the  mean. 
Hence,  the  oil  of  cassia  is  said  to  have  a  greater  dispersive 
power  than  the  glass,  because  it  spreads  or  disperses  the  spec- 
trum over  a  greater  surface  than  the  glass. 

385.  Flint-glass,  which  contains  in  its  composition  oxide  of 
lead,  has  a  greater  dispersive  power  than  crown-glass,  which 
does  not  contain  this  ingredient.     If,  therefore,  ABC,  figure 
184,  be  a  prism  of  flint-glass,  and  AFC  a  similar  one  of  crown- 
glass,  though  the  spectrum  will  disappear,  and  the  luminous 
spot,  W,  be  reproduced,  it  will  not  be  composed  of  pure  white 
light,  as  was  the  case  when  two  prisms  of  the  same  kind  of 
glass  were  used  (§  379),  but  coloured  on  one  side  with  red,  and 
on  the  other  with  purple.     This  is  occasioned  by  the  unequal 
dispersive  power  of  the  two  kinds  of  glass  producing  spectra 
of  unequal  lengths,  though  the  mean  ray  is  equally  refracted, 
by  both,  and  therefore  the  luminous  spot  produced  just  where 
it  was  before. 

336.  But  though  some  prisms  expand  the  spectrum  much  more  than 
others,  they  do  not  in  such  cases  expand  all  the  differently  coloured  bands 
equally.  The  oil  of  cassia  prism,  alluded  to  above  (§  384),  will  form  a 
spectrum  twice  as  long-  as  one  of  flint-glass ;  but  the  violet  and  indigo 
bands  will  be  much  more  expanded  in  proportion  than  the  red  and  the 
orange.  If  two  prisms,  one  of  oil  of  cassia,  and  the  other  of  sulphuric 
acid,  are  used,  this  difference,  we  are  told,  is  very  striking1, 

said  of  the  composition  of  each  of  the  colours  of  the  spectrum  besides  the 
three  primary  rays?  What  is  the  orange  chiefly  composed  of?  384.  Why 
is  the  green  sometimes  called  the  mean  ray?  Does  it  always  occupy  the 
middle  of  the  spectrum  ?  Will  the  length  of  the  spectrum  depend  upon  the 
nature  of  the  prism  used  ?  What  is  said  of  the  spectrum  produced  by  a  prism 
of  pil  of  cassia  ?  What  is  meant  by  the  dispersive  power  of  a  prism  ?  385. 
What  is  said  of  the  dispersive  power  of  a  prism  made  of  flint-glass,  as  com- 
pared with  one  of  crown-glass  ?  If  two  prisms,  similar  in  form,  but  one  of 
flint-glass  and  the  other  of  crown-glass,  are  combined  as  represented  in 
figure  184,  will  white  light  be  reproduced  as  when  two  prisms  of  the  same 
kind  of  glass  are  used  ?  What  reason  is  given  ? 

17* 


198  NATURAL     PHILOSOPHY. 

387.  The  solar  spectrum 
furnishes  the  means  of 
producing  some  of  the 
most  gorgeously  coloured 
figures  that  can  be  pre- 
sented  to  the  eye.  Let  a 
ray  of  light,  S,  from  the 
sun  be  admitted  through 
a  window-shutter,  D  E,  of 
a  darkened  room  upon  a 

glass  prism,  ABC,  as  before  ($378),  and  hold  a  little  beyond  it 
in  the  coloured  ray  a  glass  tube,  T,  about  an  inch  in  diameter, 
and  there  will  immediately  be  formed  upon  the  screen,  placed 
at  about  10  feet  distance,  an  ellipse  of  the  most  beautiful  co- 
lours, which  will  vary  with  every  motion  of  the  tube.  The 
form  will  also  vary  as  the  tube  is  held  more  or  less  inclined  in 
the  ray,  approaching,  when  it  is  held  in  one  position,  nearly  to 
a  circle,  and  when  held  in  another  position,  becoming  a  very 
elongated  ellipse. 

If  for  the  tube  other  transparent  or  reflecting  bodies  are  sub- 
stituted, regular  figures  of  every  conceivable  form  may  be 
produced,  all  of  them  displaying  the  richest  tints  of  the  rainbow. 
A  tumbler  of  cut  glass  partly  filled  with  clear  water,  substituted 
for  the  tube,  produces  some  of  the  most  beautiful  figures,  while 
the  slight  motion  of  the  water  causes  a  flashing  of  the  colours, 
occasionally  not  unlike  the  coloured  Aurora  Borealis,  some- 
times seen. 

These  experiments  are  easily  performed,  and  equal  in  bril- 
liancy anything  that  can  be  produced  in  the  whole  range  of 
optical  science.  (See  Description  by  Professor  OLMSTED,  in 
SIL.  JOUR.,  Vol.  XLVIII,  page  137.) 

388.  Fixed  Lines  of  the  Spectrum.  —  When  a  narrow  line  of 
light  is  admitted  through  a  slit  in  the  window-shutter  of  a 
darkened  chamber,  and  made  to  fall  upon  a  good  prism  of 
glass,  the  spectrum  thus  formed  will  be  crossed  throughout  its 
whole  extent  by  dark  lines  of  different  breadths,  which  can  be 
best  seen  by  a  telescope  standing  at  the  distance  of  some  10  or 
12  feet.  These  lines  can  be  better  observed  by  looking  at  the 
narrow  slit  by  which  the  light  is  admitted  through  the  prism ; 
and  the  effect  is  said  to  be  considerably  increased  if  a  bottle 
of  nitrous  acid  gas  is  interposed  between  the  glass  and  the 
light. 

None  of  these  lines  correspond  to  the  boundaries  of  the  dif- 
ferent colours,  though  the  whole  number  is  not  less  than  600. 

Qncfl.  387.  What  is  said  of  the  coloured  figures  that  may  be  produced  by 
means  of  the  solar  spectrum  ?  How  are  these  coloured  figures  produced  as 
explained  in  figure  187?  What  is  said  of  the  flashing  occasionally  produced 
when  a  tumbler  of  clear  water  is  held  in  the  spectrum?  388.  How  may  ihe 
fixed  lines  of  the  spectrum  be  seen  ?  Are  these  lines  always  the  same  for 


OPTICS!.  199 

Perhaps  the  most  important  point  connected  with  these  lines  is, 
their  constancy  for  the  same  kind  of  light,  or  light  from  the 
same  source.  Thus,  the  spectrum  formed  by  the  light  of  the 
sun,  whether  derived  directly  or  indirectly  from  their  source, 
always  exhibits  the  same  lines;  but  almost  every  fixed  star 
has  its  own  system  of  lines.  But  the  spectra  formed  by  the 
light  of  the  stars  Sirius  and  Castor  are  precisely  alike. 

It  is  a  little  remarkable  that  the  spectrum  formed  by  lamp- 
light contains  none  of  these  dark  lines;  but  in  some  cases  dis- 
tinct bright  lines  appear  instead  of  them. 

389.  Illuminating  Power  of  the   Spectrum.  —  The  greatest 
illuminating  power  of  the  spectrum  appears  to  be  in  the  yellow 
band,  and  from  this  it  decreases  towards  both  extremities. 
The  best  method  to  determine  this  point  is  to  throw  the  spec- 
trum upon  a  screen  on  which  is  some  tolerably  fine  print,  and 
observe  where  the  print  can  be  read  most  distinctly. 

For  a  discussion  of  the  heating  rays,  and  also  the  chemical 
rays,  which  always  accompany  the  several  coloured  rays  of 
the  spectrum,  see  author's  Chemistry,  pages  64  and  65. 

390.  Colours  of  Bodies.  —  The  colour  of  a  body  is  not  the 
result  of  anything  naturally  inherent  in  the  body  itself,  but  de- 
pends upon  its  relations  to  light.   Whatever  may  be  the  colour 
of  a  body,  when  held  in  the  red  ray  of  the  spectrum,  it  is  itself 
red ;  and  when  held  in  the  blue,  it  is  blue,  &c. ;  the  colour  in 
any  case  being  of  course  more  brilliant  when  the  natural  colour 
of  the  body  corresponds  with  the  colour  of  the  ray  in  which  it 
is  held.  A  red  wafert  for  instance,  when  held  in  the  red,  is  red, 
and  when  held  in  the  yellow,  is  yellow;  but  the  red  is  more 
brilliant  than  the  yellow,  because  the  natural  colour  of  the 
wafer  corresponds  with  the  colour  of  the  ray.    The  colour  of  a 
body,  therefore,  is  the  colour  simply  of  the  light  it  reflects.     A 
red  substance  is  one  that  has  the  power  of  reflecting  the  red, 
while  it  absorbs  or  stifles  all,  or  nearly  all,  the  other  rays;  a 
green  substance  is  one,  the  surface  of  which  reflects  the  green, 
while  it  absorbs  the  other  rays,  and  so  of  the  other  colours. 
The  different  shades  of  tints  observed  in  bodies  are  all  occa- 
sioned by  different  mixtures  of  the  primary  rays. 

Bodies  that  reflect  all,  or  nearly  all  the  light  which  falls  upon 
them,  are  white,  while  those  that  absorb  nearly  all  are  black. 
But  probably  no  substance  is  capable  either  of  reflecting  or 
absorbing  all  the  rays  that  fall  upon  them. 

light  of  the  same  kind  ?  What  is  said  of  the  lines  seen  in  the  light  of  different 
fixed  stars  ?  Are  these  lines  seen  in  the  spectrum  formed  by  the  light  of  a 
lamp  ?  389.  Where  is  found  the  greatest  illuminating  power  of  the  spectrum  ? 
390.  Upon  what  does  the  natural  colour  of  a  body  depend  ?  Will  any  body, 
whatever  its  colour,  when  held  in  one  of  the  rays  of  the  spectrum,  appear  of 
the  same  colour  as  that  ray  ?  Why  will  a  red  wafer,  when  held  in  the  red 
ray,  appear  of  a  more  brilliant  colour  than  when  held  in  any  other  ray? 
What  then  is  the  colour  of  a  body  ?  When  is  the  colour  of  a  substance  said 
to  be  red  ?  When  is  it  said  to  be  green  ?  Upon  what  do  the  different  shades 
of  tint,  observed  in  bodies,  depend  ?  When  will  a  body  be  white  ?  When  black  ? 


200  NATURAL     PHILOSOPHY. 

391.  Newton  attempted  to  account  for  the  particular  colour 
reflected  by  a  body,  by  supposing  it  to  depend  upon  the  size 
of  its  particles.    He  found  that  on  pressing  a  large  convex  lens 
upon  a  plate  of  glass,  at  the  central  point  where  the  two  pieces 
of  glass  touched,  a  black  spot  was  produced,  but  immediately 
around  this  rings  were  formed,  possessing  all  the  different 
colours  of  the  spectrum  ;  and  that  the  production  of  a  particular 
tint  depended  upon  the  thickness  of  the  stratum  of  air  inter- 
vening between  the  glasses.     So  also,  when  soap-bubbles  are 
blown  very  thin,  they  exhibit  the  same  beautifully  coloured 
rings,  particularly  around  the  top,  just  before  they  burst.     In 
both  these  cases  the  different  colours  appear  to  be  produced 
by  the  different  thicknesses  of  the  film  of  air,  and  of  solution 
of  soap,  at  the  points  where  they  are  produced.     Thus,  in  the 
experiment  with  the  two  glasses,  at   the  centre  where  the 
glasses  touch,  the  colour  is  black ;  but  at  a  little  distance  where 
the  film  of  air  is  of  a  certain  thickness,  a  particular  colour, — 
suppose  blue,— is  produced.  Still  further  from  the  central  point, 
where  the  film  of  air  becomes  of  another  determinate  thick- 
ness, some  other  colour,  as  yellow,  is  seen ;  and  so  for  every 
variation  in  the  thickness  of  the  film  or  plate  of  air,  a  different 
colour  is  produced.     And  as  the  apparatus  is  simply  a  double 
convex  lens  pressed  upon  a  piece  of  plate-glass,  it  is  evident,  that 
at  every  given  distance  from  the  central  point  of  contact,  the  films 
of  air  of  the  same  thickness  will  constitute  circles;  the  colours 
will  be  in  the  form  of  rings,  as  is  always  the  case,  unless  the 
glasses  are  pressed  together  more  on  one  jside  than  the  other. 

392.  It  appears,  then,  that  when  certain  substances  are  re- 
duced to  very  thin  plates,  they  have  the  power  of  decomposing 
light,  and  reflecting  only  certain  of  the  rays,  while  the  others 
are  transmitted  or  absorbed ;  and,  if  we  could  obtain  one  of 
these  plates  or  films  of  uniform  thickness,  its  tint  would  be  uni- 
form throughout.   Now,  we  may  suppose  all  bodies  to  be  com- 
posed of  such  films,  which,  though  they  are  in  contact,  may 
still  act  upon  light  in  the  same  manner  as  if  they  were  separate. 
Their  colour  would,  of  course,  be  the  colour  of  the  light  re- 
flected by  their  external  film,  the  thickness  of  which,  we  may 
suppose,  would  depend  upon  the  size  of  the  particles  of  the 
body.  From  this  it  follows,  therefore,  that  the  colour  of  a  body 
will  depend  upon  the  size  of  its  particles.     But  it  is  to  be  re- 

Quest.  391.  Upon  what  did  Newton  suppose  the  particular  colour  reflected 
by  a  body  to  depend  ?  What  did  he  find  was  produced  when  a  convex  lens 
was  pressed  upon  a  piece  of  glass  with  a  plane  surface  ?  What  does  the 
production  of  a  particular  tint  in  this  experiment  depend  upon  ?  What  is  said 
of  the  colours  produced  when  soap-bubbles  are  blown  very  thin  ?  In  these 
two  experiments,  will  a  particular  tint  be  produced  for  any  different  thick- 
ness of  the  film  of  air  or  of  solution  of  soap  ?  Why,  in  the  experiment  with 
the  lens  and  plate  of  glass,  will  all  the  several  colours  be  arranged  in  circles  ? 
392.  If  we  could  obtain  a  film  of  a  transparent  substance  of  uniform  thick- 
ness, would  its  tint  be  uniform  throughout  ?  May  we  suppose  all  bodies  to 
be  composed  of  such  films  which  act  upon  light  just  as  if  they  were  separated  ? 


OPTICS.  201 

membered  that  this  method  of  accounting  for  the  particular 
colour  reflected  by  a  body  is  merely  theoretical,  and  is  not  to 
be  considered  as  established. 

393.  Some  substances  that  are  of  themselves  opake,  or  nearly 
so,  become  transparent,  or  at  least  translucent,  by  being  moist- 
ened with  some  transparent  fluid.     Thus,  common  writing- 
paper,  especially  when  tolerably  thick,  is  quite  opake;  but  it 
becomes  very  translucent  when  saturated  with  oil.     This  is  oc- 
casioned by  the  filling  of  the  pores  of  the  paper  with  the  oil,  by 
which  the  light  is  transmitted,  though  it  was  incapable  of  pass- 
ing these  mfnute  interstices  when  void,  or  filled  only  with  air. 

394.  The  Rainbow  — The  rainbow  is  a  splendid  natural  phe- 
nomenon, consisting  of  a  coloured  arch  apparently  suspended 
in  the  sky,  usually  seen  after  a  shower  of  rain  in  that  part  of 
the  heavens  opposite  to  the  sun.    When  the  circumstances  are 
favourable  there  are  always  two  bows,  one  within  the  other, 
the  inner  one  being  brightest,  and  therefore  called  the  primary 
bow.     The  other  is  called  the  secondary  bow. 

395.  The  rainbow  is  also  sometimes  seen  in  the  spray  pro- 
duced by  a  cataract,  as  at  Niagara  Falls,  or  by  the  dashing  of 
the  waves  upon  the  shore  of  the  ocean.     But  in  all  cases  the 
cause  is  the  same,  viz:  the  decomposition  of  the  light  of  the 
sun  by  the  falling  drops  of  water  in  the  manner  of  the  prism 
(§  378),  and  its  subsequent  reflection  to  the  eye  of  the  observer. 
The  position  of  the  bow,  whether  seen  in  the  drops  of  falling 
rain,  or  in  the  spray  of  the  cataract,  will  always  be  on  the  op- 
posite side  of  the  observer  from  the  sun ;  that  is,  in  looking  at 
the  bow  in  front  of  him,  he  will  have  the  sun  behind  him.     On 
further  examination,  it  will  be  found  that  the  sun,  the  eye  of 
the  observer,  and  the  centre  of  the  circle  of  which  the  bow 
forms  a  part,  will  be  in  the  same  straight  line. 

396.  To  understand  the  manner 
in  which  the  light  is  decomposed 
and  reflected  to  the  eye,  let  us  sup- 
pose  ABC,  figure  188,  to  be  a  drop 
of  water  suspended  in  the  air,  and 
S  a  ray  of  light  from  the  sun  to 
strike  it  at  A.  As  the  water  is  more 
.  ]88.  dense  than  the  air  in  which  the  ray 

What  then  would  be  the  colour  of  a  body  ?  What  may  we  suppose  the  thick- 
ness of  the  films  of  a  body  to  depend  upon  ?  Are  we  to  consider  this  expla- 
nation of  the  colours  of  bodies  as  demonstrated  ?  393.  How  may  some  opake 
bodies  be  made  translucent  ?  Why  does  paper  become  translucent  when  its 
pores  are  filled  with  oil  or  water?  394.  What  does  the  rainbow  consist  of? 
In  what  part  of  the  heavens  is  it  seen  ?  How  many  bows  are  seen  when  the 
circumstances  are  favourable  ?  By  what  terms  are  these  two  rainbows  dis- 
tinguished ?  395.  In  what  is  the  rainbow  sometimes  seen  ?  Is  the  cause 
always  the  same  ?  Will  the  bow  always  be  seen  on  the  side  of  the  observer 
opposite  the  sun  ?  What  is  said  of  the  relative  positions  of  the  sun,  the  eye 
of  the  observer,  and  the  centre  of  the  bow  ?  396.  What  will  be  the  course 
of  the  ray  in  the  drop  of  water  as  illustrated  in  figure  188  ?  If  it  were  possi  - 


202  NATURAL     PHILOSOPHY. 

has  been  moving,  on  entering  the  drop,  instead  of  proceeding 
onward  in  a  straight  line  to  D,  it  will  be  bent  downward  to  B, 
and  then  from  the  interior  surface  it  will  be  reflected  back  to 
C ;  and  on  emerging  into  the  air  again  at  C,  it  will  be  bent 
upward  and  proceed  to  O,  as  if  coming  from  D.  Now,  the  white 
light  of  the  sun's  ray  is  always  decomposed,  more  or  less,  when 
refracted;  consequently,  at  A,  some  separation  of  the  primary 
rays  must  take,  which,  however,  will  be  increased  at  C.  From 
a  single  drop,  therefore,  all  the  colours  of  the  spectrum  will 
be  produced,  the  violet,  as  it  is  most  refracted  (§  337),  being 
highest,  and  the  red  lowest,  with  the  other  rays  between  them. 
If  it  were  possible,  therefore,  to  suspend  a  single  drop  of  water 
in  the  air,  as  supposed,  at  the  distance  at  which  the  bow  is 
formed,  and  to  receive  on  a  screen  in  a  dark  chamber  the  se- 
veral rays  thus  decomposed  and  reflected  from  it,  we  should 
form  a  solar  spectrum,  as  perfect  as  that  produced  by  the 
prism,  only  it  would  be  exceedingly  faint,  because  of  the  small 
quantity  of  light  Now,  if  we  place  the  eye  in  the  solar  spec- 
trum produced  by  the  prism,  as  a  general  thing,  only  one  ray 
can  enter,  the  other  rays  all  passing  either  above  or  below  the 
eye.  So  of  the  coloured  rays  separated  by  the  drop  of  water 
in  the  air,  only  one  of  them  could  be  seen  by  the  eye  while  in 
the  same  position,  but  they  could  all  be  seen  in  succession  by 
raising  or  depressing  the  eye. 

397.  But  let  us  suppose  there  are 
several  drops  placed  side  by  side 
one  above  the  other,  as  A,  B,  C, 
figure  189.  To  prevent  confusion, 
we  will  trace  the  course  of  only 
three  rays,  the  violet,  the  yellow, 
and  the  red.  Let  S  S  S  be  the  rays 
of  the  sun,  which  will  be  parallel. 
From  the  uppermost  drop,  A,  the 
several  colours  will  emerge,  as 
above  described;  but  the  violet 
and  yellow  will  pass  above  the 
eye  at  E,  the  red  only,  which  is 
least  refracted,  entering  it.  The 
drop,  A,  therefore,  will  appear  en- 
tirely  red.  Of  the  rays  from  the 
next  drop,  B,  the  yellow  only,  we 
will  suppose,  enters  the  eye.  the  position  of  the  drop  being 

ble  to  suspend  a  single  drop  of  water  in  the  heavens  at  the  proper  distance, 
would  it  give  all  the  colours  of  the  spectrum  ?  If  the  eye  is  placed  in  the 
polar  spectrum  formed  by  the  prism,  why  will  only  one  colour,  as  a  general 
thing,  be  seen  ?  Would  only  one  of  the  colours  produced  by  the  drop  of 
water  be  seen  ?  397.  But  if  there  are  several  drops  perpendicularly  over 
each  other,  what  will  be  the  effect  ?  What  three  colours  are  supposed  to  be 
reflected  to  the  eye  from  the  three  drops  in  figure  189?  Why  does  the  eye 


OPTICS.  203 

such  as  to  bring  this  to  the  eye,  while  the  two  extreme  rays 
pass  one  above,  and  the  other  below  it.  This  drop,  therefore, 
will  appear  yellow.  From  the  lowest  drop,  C,  only  the  most  re- 
fracted ray,  the  violet,  will  enter  the  eye;  all  the  others  not  being 
bent  upward  sufficiently,  passing  below  it.  Its  colour,  there- 
fore, would  be  violet.  It  will  be  seen,  therefore,  though  the 
several  coloured  rays  which  emerge  from  each  drop,  reckoning 
downwards,  would  be  in  the  order  violet,  yellow,  and  red,  yet 
to  the  observer,  looking  at  them  in  their  position,  this  order 
would  be  reversed ;  and  he  would  see  the  red  highest,  then  the 
yellow  below  it,  and  then  the  violet  lowest.  Now  this  is  the 
order  in  which  the  colours  are  always  seen  in  the  primary 
rainbow ;  the  red  occupies  the  highest  or  outside  edge  of  the 
bow,  and  the  violet  the  inside,  the  other  colours  being  inter- 
mediate in  regular  order  between  them. 

398.  It  is  evident  that  in  the  production  of  the  rainbow,  drops 
of  water  cannot  remain  suspended  in  the  air,  as  we  have  sup- 
posed, but  the  effect  is  the  same.     The  drops  are  indeed  con- 
stantly falling,  but  at  any  point  from  which  a  particular  ray 
comes  to  the  eye,  they  succeed  each  other  with  such  rapidity, 
that  the  effect  is  the  same,  in  decomposing  the  light,  as  if  a  sin- 
gle drop  had  remained  suspended  there. 

399.  Exterior  to  the  primary  bow,  and  at  a  distance  from  it, 
is  the  secondary  rainbow,  which  is  always  less  brilliant  than 
the  primary,  and  has  the  several  colours  in  the  reverse  order. 
That  is,  in  the  secondary  bow  the  violet  is  outermost,  and  the 
red  on  the  inside  edge,  with  the  other  colours  in  their  proper 
order  between  them. 

To  understand  the  mode  in 
which  this  is  formed,  let  A  B  C  D, 
figure  190,  be  a  drop  of  water, 
and  S,  a  ray  of  white  light  from 
the  sun,  entering  it  at  D.  On 
entering  the  water,  by  the  law 
of  refraction  it  will  be  bent  up- 
ward to  C,  from  which  it  will 
be  reflected  by  the  interior  sur- 
Fig  190  face  to  B,  and  from  that  to  A, 

where  it  will  again  emerge  into 

the  air,  and  will  be  bent  downward  to  E,  the  several  coloured 
rays  being  separated  from  each  other  as  before.  In  this  case, 
however,  the  red,  being  least  refracted,  will  be  uppermost,  and 
the  violet  lowest.  And  if  we  suppose  several  drops  to  be  ar- 

receive  only  the  red  from  the  first  or  uppermost  drop  ?  And  why  is  the  violet 
ray  only  received  from  the  lowest  drop  ?  What  becomes  of  the  other  rays? 
What  is  the  order  in  which  the  colours  always  appear  in  the  primary  rain- 
bow ?  198.  Do  drops  of  water  actually  remain  suspended  in  the  air  in  this 
manner  ?  How  then  are  the  colours  formed  ?  399.  Where  is  the  secondary 
rainbow  situated  in  reference  to  the  primary  bow  ?  What  is  the  order  of  the 


204  NATURAL     PHILOSOPHY. 

ranged  above  each  other  as  before  ($  395),  it  is  easy  to  see  that 
the  order  of  the  colours  must  be  the  reverse  of  that  in  the  pri- 
mary rainbow,  as  is  really  the  case  in  the  secondary  bow. 

,S  The  position  of  the  two  rainbows, 
and  the  order  of  the  colours  in  each, 
will  be  as  represented  in  figure  191. 
S  S  are  the  rays  of  the  sun,  and  E 
the  eye  of  the  observer.  The  ex- 
treme colours  only,  the  red  and  the 
violet,  are  represented,  the  others 
being  supposed  in  their  proper  order 
between  them. 

400.  It  will  be  observed  that  in  the 
production  of  the  primary  rainbow 
the  light  undergoes  two  refractions, 
one  on  entering  the  drop  of  water, 
and  the  other  on  leaving  it,  and  one  reflection ;  but  in  the  se- 
condary bow  it  is  twice  refracted,  once  on  entering  the  drop, 
and  again  on  leaving  it,  as  before,  and  twice  reflected.  Now 
at  every  refraction  and  every  reflection,  a  portion  of  the  light 
is  necessarily  lost;  we  see,  therefore,  why  the  colours  of  the 
secondary  bow  should  be  less  brilliant  than  those  of  the  pri- 
mary, the  light  in  producing  it  having  to  undergo  one  more 
reflection.  Other  rainbows,  besides  these  two,  are  theoretically 
possible,  in  forming  which  the  light  must  undergo  more  than 
two  reflections  in  the  drops  of  water,  but  the  colours  become 
by  so  many  reflections  too  faint  to  be  observed. 

401.  As  the  sun,  the  eye  of  the  spectator,  and  the  centre  of 
the  bow,  must  always  be  in  a  straight  line,  we  perceive  why 
the  rainbow  is  seen  in  time  of  rain  only  in  the  morning  or 
evening.  Suppose  a  rain-cloud  to  pass  over  the  observer  as 
early  as  3  o'clock  in  the  afternoon,  with  well-defined  edges,  so 
that  the  sun  makes  his  appearance  as  soon  as,  or  even  a  little 
before,  the  rain  has  ceased  falling  at  the  point  where  he  is 
standing;  a  line  drawn  from  the  sun  through  his  eye,  on  ac- 
count of  the  sun's  being  so  high  in  the  heavens,  would,  if  con- 
tinued, strike  the  ground  so  near  him  as  not  to  allow  of  the 
formation  of  the  bow. 

The  altitude  of  the  sun  above  the  horizon  where  the  primary 
bow  is  seen  by  an  observer  situated  upon  the  level  surface  of 
the  earth,  cannot  be  more  than  about  41  or  42  degrees;  but  if 
the  observer  be  upon  a  high  mountain,  he  may  often  see  it 
formed  below  him  when  the  sun  is  higher  in  the  heavens.  So, 

colours  in  the  secondary  bow?  What  is  shown  in  figure  190?  What  is 
shown  in  figure  191  ?  400.  How  many  reflections  and  refractions  does  the 
light  undergo  in  producing  the  primary  rainbow  ?  How  many  in  producing 
the  secondary  bow?  Why  is  the  secondary  bow  less  brilliant  than  the 
primary?  Are  other  rainbows  possible  ?  Why  are  they  not  seen  ?  401.  Why 
is  the  rainbow  seen  only  morning  or  evening  ?  What  is  the  greatest  altitude 


OPTICS.  205 

if  the  observer  be  on  a  plain,  the  magnitude  of  the  bow  cannot 
exceed  a  semicircle,  but  it  is  not  so  to  a  person  on  a  high 
mountain. 

Rainbows  are  sometimes  formed  by  the  light  of  the  moon, 
but  the  colours  are  exceedingly  faint,  so  as  to  be  scarcely  per- 
ceptible. 

402.  The  circles  often  seen  around  the  sun  and  moon  are 
produced  by  different  refractions  and  reflections  of  the  light, 
in  passing  through  the  particles  of  moisture  and  other  exhala- 
tions, contained  in  the  atmosphere.  Sometimes  it  is  supposed 
they  are  occasioned  by  small  crystals  of  ice,  which  are  no 
doubt,  even  in  warm  weather,  often  produced  by  the  cold 
which  is  known  to  prevail  in  the  upper  regions  of  the  atmo- 
sphere. Sometimes  several  circles  are  seen  at  once  around 
the  sun  or  moon,  but  they  do  not  usually  have  the  same  centre, 
which  for  each  circle  is  at  a  little  distance  from  the  luminary. 
When  there  is  but  a  single  circle,  the  luminary  always  appears 
exactly  in  its  centre.  Not  unfrequently,  besides  the  circles 
surrounding  the  luminary,  several  other  circles  and  parts  of 
circles  are  seen  crossing  each  other  in  various  directions,  some 
of  which  will  have  the  luminary  in  their  circumferences,  and 
some  will  be  at  a  distance  from  it,  and  apparently  having  no 
connection  with  it.  To  all  these  the  term  halo  has  been  indis- 
criminately applied.  Mock  suns  or  coronce  appear  to  be  usually 
only  small  fragments  of  arcs  of  circles,  and  are  generally  seen 
in  pairs  at  equal  distances  from  the  sun,  on  opposite  sides. 

Fisr.  192  is  a  representation  of  the  halo  which  was  seen  in 
the  State  of  Connecticut,  and  other  parts  of  our  country,  about 
the  middle  of  the  day,  September  9,  1844.  It  is  made  from  a 
sketch  taken  by  the  eye  at  the  time,  the  observer  being  sup- 
posed to  face  the  south.  Around  the  sun,  S,  were  two  distinct 
circles*  not  concentric  with  each  other ;  and  at  A  and  B,  above 
and  below  the  sun,  where  these  circles  crossed  or  overlaid 
each  other,  were  two  bright  coronae.  North  of  the  sun,  and 
having  the  sun  in  its  circumference  at  the  south,  was  the  large 
circle  S  D  C  E,  which  was  very  distinct  and  fully  formed.  At 
C,  the  segments  of  two  other  circles  appeared  crossing  each 

the  sun  can  have  when  the  primary  bow  is  seen  ?  If  the  observer  is  standing 
on  "a  plain,  what  is  the  greatest  magnitude  the  bow  can  have  ?  May  rain- 
bows be  formed  by  the  light  of  the  moon  ?  402.  How  are  the  circles  often 
seen  around  the  sun  and  moon  produced  ?  May  crystals  of  ice  exist  in  the 
upper  regions  of  the  atmosphere  in  places  in  warm  latitudes  ?  Are  there 
sometimes  more  than  one  circle  ?  What  are  mock-suns  ?  Where  was  the 
halo  seen  represented  in  figure  192?  Did  any  of  these  circles  exhibit  the 

*  It  is  proper  to  state  that  in  an  article  which  appeared  in  the  New  Haven 
Palladium  the  next  day  after  the  occurrence  of  this  phenomenon,  these  were 
described  as  a  "circle  accompanied  by  an  ellipse  of  the  same  major  axis, 
and  of  small  eccentricity  ;"  but,  without  attempting  now  to  decide  the  ques- 
tion, the  writer  has  thought  best  to  follow  his  own  notes  made  at  the  time. 
18 


206  NATURAL     PHILOSOPHY. 


Fig.  192. 

other,  and  also  the  circle  S  D  C  E.  These  segments  were  very 
distinct,  but  the  rest  of  the  circles,  of  which  they  formed  a  part, 
indicated  by  the  dotted  lines,  though  at  times  perceptible,  were 
very  faint.  The  two  circles  around  the  sun  at  times  exhibited 
the  colours  of  the  rainbow  with  considerable  vividness,  but 
all  the  others  were  white.  At  Jackson,  Tennessee,  a  combina- 
tion of  circles  very  similar  to  these  was  seen  January  1st,  1824. 
(Sil.  Journal,  Vol.  VII.,  p.  384). 

403.  A  very  singular  phenomenon,  called  mirage  or  fata 
worgana,  which  is  occasionally  seen  in  different  countries, 
appears  to  be  occasioned  by  a  peculiar  state  of  the  atmosphere 
in  the  place,  the  lower  parts  near  the  surface  being  much  more 
dense,  and  of  course  refracting  the  light  more  (§  360)  than  the 
parts  immediately  above.  This,  as  we  have  seen,  always  takes 
place  to  some  extent ;  but  in  some  cases,  from  the  operation 
of  causes  which  are  not  altogether  understood,  the  difference 
in  the  density  of  the  lower  and  upper  parts  of  the  atmosphere 
becomes  greatly  increased ;  and  rays  of  light  from  objects  at 
the  surface,  which  are  at  first  emitted  in  a  direction  that  would 
carry  them  high  above  the  earth,  are,  by  the  unequal  refraction 
of  the  different  strata  of  the  atmosphere,  gradually  bent  so 
much  out  of  their  original  course  as  to  be  again  returned  to 

colours  of  the  rainbow?  403.  What  occasions  the  phenomenon  called 
mirage  or  fata  morgana  ?  May  the  density  of  the  air  above  us  diminish  so 
rapidly  as  to  cause  rays  of  light  from  distant  objects  that  would  otherwise 
pass  over  our  heads  to  be  brought  down  to  the  eye  ?  Will  an  image  of  the 
object  be  then  seen  in  the  air  ?  How  is  this  illustrated  in  figure  193  ? 


OPTICS. 


207 


the  surface.   In  such  a  case  an  image  of  the  object  will  be  seen, 
more  or  less  elevated  above  the  object  itself,  in  the  direction 
of  the  rays  as  they  enter  the  eye  ($  360). 
. ,  /.  Thus,  let  A  B  be  an  object 

in  the  horizon  seen  directly 
by  the  eye,  E,  by  the  rays 
AE  and  BE,  through  the 
strata  of  air  near  the  surface 
of  uniform  density.  At  the 
same  time,  rays  will  be  emit- 
ted in  other  directions,  as 
A  m,  and  B  n ;  and  if  the  den- 
sity of  the  air  through  which 
Fjg-  m  these  rays  pass  diminishes 

with  sufficient  rapidity,  they  may  be  bent  so  much  out  of  their 
original  course  as  to  be  brought  down  to  the  eye,  E,  of  the 
spectator,  and  he  will  see  an  image  of  the  object  in  the  air  as 
A'B'. 

404.  If  the  density  of  the  air  through  which  the  ray  Bn 
passes,  diminishes  much  more  rapidly  than  that  through  which 
the  ray  A  m  passes,  B  n  may  be  bent  downward  more  than 
A  m,  so  as  to  cross  it;  and  then  the  image  A'  B'  will  be  invert- 
ed. In  many  instances,  a  direct  and  an  inverted  image,  one 
above  the  other,  have  been  seen  at  the  same  time. 

This  phenomenon  may  occur  when  the 
object,  the  image  or  images  of  which  are 
seen  in  the  air,  are  below  the  horizon. 
Figure  194  represents  a  phenomenon  of 
this  kind,  which  was  seen  by  Dr.  Yince 
from  Ramsgate,  a  small  town  on  the  coast 
of  England.  A  ship  was  passing  at  such  a 
distance,  that  only  her  topmasts,  A,  appear- 
ed above  the  horizon  ;  but  in  the  air  above 
the  ship  were  two  perfect  images  of  her,  B, 
and  C,  the  lower  one  of  which  was  invert- 
ed and  the  other  erect,  the  keels  of  the  two 
being  together.  In  another  case  of  the  kind, 
there  appeared  a  portion  of  the  sea  between 
the  two  images. 

In  1822,  a  young  English  captain,  being 
at  sea,  observed  the  inverted  image  of  a 
ship  in  the  air,  which  was  so  distinct  that 
he  recognised  it  as  the  one  commanded  by 


Fig.  194. 


his  father,  though  the  ship  at  the  time  was  entirely  out  of  sight 
below  the  horizon. 

Quest.  404.  Under  what  circumstances'  will  the  image  appear  inverted  ? 
May  this  phenomenon  occur  when  the  object,  the  image  of  which  is  formed 
in  the  air,  is  below  the  horizon  ?  What  is  represented  in  figure  194  ?  What 
is  said  of  the  English  sea-captain  ? 


208  NATURAL     PHILOSOPHY. 

405.  The  ship  that  was  seen  coming  into  the  harbour  of  New- 
Haven,  Connecticut,  in  the  month  of  June,  1647,  was,  no  doubt, 
an  instance  of  this  kind.     This  town  was  first  settled  in  1037; 
and  only  10  years  afterwards,  with  much  effort,  the  citizens 
fitted  out  their  first  ship  of  about  150  tons,  which  sailed  for 
England  in  January,  1647.  This  was  of  course  to  them  a  matter 
of  great  importance,  especially  as  she  took  as  passengers  several 
of  their  first  inhabitants.     On  the  opening  of  spring  they  were 
greatly  disappointed  to  learn  by  arrivals  from  England  that 
nothing  had  been  heard  of  her  there,  and  of  course  were  in  a 
dreadful  state  of  suspense  with  regard  to  her.     In  the  month 
of  June,  after  a  severe  shower  of  rain,  attended  with  lightning 
and  thunder,  a  little  before  sunset,  it  was  announced  to  their 
great  joy  that  a  ship  of  similar  dimensions  to  their  own  was 
entering  the  harbour,  and  sailing  up  to  the  town.     She  con- 
tinued thus  to  advance  towards  the  town,  nearly  in  a  north 
direction,  with  all  her  sails  set,  for  nearly  half  an  hour,  though 
the  wind  was  directly  against  her;  until  at  length,  when  arriving 
very  near  the  spectators  who  had  assembled  to  see  her,  the 
tops  of  her  masts  seemed  to  be  blown  off,  then  other  portions 
of  her  masts  and  rigging,  and  in  a  few  minutes  the  whole  ship 
had  disappeared ! 

The  feelings  likely  to  be  produced  in  the  minds  of  the  people 
by  such  an  occurrence,  at  such  a  time,  and  under  such  circum- 
stances, may  easily  be  imagined.  Nor  is  it  wonderful  they 
should  conclude  that  a  kind  Providence  had  taken  this  method 
"  for  the  quieting  of  their  afflicted  spirits,"  to  intimate  to  them 
the  fate  which  had  befallen  their  beloved  ship,  and  lamented 
fellow-citizens. 

The  ship  seen  by  them  was,  no  doubt,  the  image  of  a  ship, 
formed  in  the  air  in  the  manner  explained  above,  which  was 
sailing  by  at  the  time,  but  so  distant  as  to  be  beyond  the  hori- 
zon. Her  disappearance  in  so  singular  a  manner  was  probably 
occasioned  by  the  breaking  up  of  the  strata  of  air,  which,  by 
its  unusual  refraction,  had  produced  the  phenomenon. 

406.  In  Egypt  and  other  countries,  a  different  kind  of  mirage 
is  often  seen.     The  traveller  passing  over  the  burning  sands, 
on  approaching  a  village,  sees,  as  he  supposes,  a  vast  lake  of 
water  spread  out  before  him,  from  the  surface  of  which  all 
objects  beyond  are  beautifully  reflected,  precisely  as  from  the 
surface  of  tranquil  water.     This  is  occasioned  by  the  strata  of 
air  at  the  surface  becoming  suddenly  heated,  by  its  proximity 
to  the  heated  sand,  and  rendered  less  dense  than  the  air  above 
it ;  the  rays  of  light  from  distant  objects  and  from  the  sky  are 
then  bent  upward,  and  brought  to  the  eye  just  as  if  reflected 
from  the  plane  surface  of  a  smooth  Jake.     As  the  traveller  ap- 

Quest.  405.  What  were  the  circumstances  that  occurred  at  New  Haven 
in  June,  1647  ?  How  are  these  occurrences  accounted  for  ?  406.  What  is 
said  of  the  occurrence  of  mirage  in  Egypt  ?  How  are  they  explained  ?  Why 


OPTICS.  209 

preaches  the  village,  the  supposed  lake  of  course  vanishes,  and 

nothing  appears  but  the  same  burning  sands  he  has  for  hours 

perhaps  been  passing  over. 

Let  AB,  figure  195, 
be  an  object  seen  at  a 
distance  by  the  rays, 
AE,  and  BE ;  other  rays, 
as  A  m  and  B  n,  pass- 
ing downward  through 
heated,  and  therefore 
less  dense  strata  of  air, 

Fig  195  are   refracted    upward 

to  the  eye  at  E,  causing 

an  inverted  image  of  the  object  to  appear  at  A'  B'. 

407.  That  the  above  is  the  true  explanation  of  these  singular 
phenomena  may  be  shown  by  direct  experiment.  Let  a  square 
phial  be  partly  filled  with  a  very  dense  and  perfectly  clear 
solution  of  sugar,  and  above  it  introduce  carefully  an  equal 
quantity  of  pure  water.    The  solution  of  sugar,  being  more 
dense  than  the  water,  will  remain  at  the  bottom ;  but  the  two 
will  mix  more  or  less  at  the  surface  of  contact,  and  form  a 
stratum,  the  density  of  which  will  diminish  upward.    If,  now, 
a  small  object,  as  a  card  with  a  word  written  upon  it,  be  held 
on  the  further  side  of  the  phial,  the  word  will  appear  in  its 
natural  position  when  viewed  through  the  water  or  the  sugar 
solution,  but  when  seen  through  the  mixed  liquid,  it  will  be 
inverted,  and  out  of  its  true  place. 

The  intelligent  student  will  observe  that  these  phenomena  of  mirage 
are  only  extreme  cases  of  atmospheric  refraction  of  the  same  kind  as 
those  described  above  (§  364),  and  are  therefore  very  properly  termed  cases 
of  extraordinary  or  unusual  refraction. 

POLARIZATION    OF    LIGHT. — DOUBLE   REFRACTION. 

408.  The  polarization  of  light  is  a  difficult  branch  of  the 
science  of  optics,  and  only  a  few  of  its  more  important  princi- 
ples can  be  discussed  in  an  elementary  work  like  the  present. 

Polarization  of  Light  by  Reflection. — If  a  beam  of  light  from 
the  sun  be  admitted  into  a  dark  room  through  a  circular  aper- 
ture in  the  window-shutter,  and  a  little  fine  dust,  as  powdered 
starch,  or  chalk  diffused  through  the  air,  or  even  the  dense 
smoke  of  burning  paper,  the  beam  will  be  seen  by  the  reflection 
of  the  light  from  the  floating  particles  to  be  everywhere  circular, 
and  will  appear  like  a  perfectly  straight  cylindrical  rod,  drawn 
across  the  room.  If  we  hold  a  piece  of  paper  in  the  beam,  a  cir- 

does  the  lake  disappear  as  the  traveller  approaches  it  ?  407.  May  this  pheno- 
menon be  imitated  by  an  experiment  ?  How  is  it  done  ?  Are  these  pheno- 
mena to  be  considered  as  extreme  cases  of  ordinary  refraction  ?  408.  When 
a  ray  of  light  from  the  sun  is  admitted  into  a  darkened  room  in  which  some 
fine  dust  or  smoke  is  diffused,  what  appearance  does  it  present  ? 


210  NATURAL     PHILOSOPHY. 

cular  luminous  spot  will  be  produced  of  the  same  size  or  a  little 
larger  than  the  aperture  through  which  the  light  is  admitted. 

409.  If  a  piece  of  window-glass,  previously  coated  on  one 
side  with  black  varnish,  be  now  held  in  the  beam  of  light,  it 
may  be  reflected  with  equal  facility  in  any  direction — upward 
to  the  ceiling,  downward  to  the  floor,  or  to  the  right  or  left. 
That  is,  it  possesses  the  same  property  on  every  side ;  for  it 
will  be  convenient  to  speak  of  the  beam  of  light  as  having  a 
right  and  left,  an  upper  and  an  under  side. 

410.  But  if  the  beam  of  light,  after  its  admission  into  the 
chamber,  instead  of  being  allowed  to  pass  directly  across,  is 
made  to  fall  at  the  proper  angle  on  a  piece  of  glass  painted 
black  on  one  side,  and  laid  on  a  table  with  its  unpainted  side 
upward,  the  beam  now  reflected  from  it  will  be  found  to  have 
undergone  a  remarkable  change.   It  may  now  be  reflected  up- 
ward or  downward  by  another  piece  of  painted  glass,  as  before, 
but  cannot  be  reflected  to  the  right  or  left.     That  is,  its  right 
and  left  sides  possess  peculiar  properties,  by  reason  of  which 
it  refuses  to  be  again  reflected  in  these  directions,  and  the  light 
is  said  to  be  polarized. 

411.  When,  as  in  this  case,  the  ray  of  polarized  light  cannot 
be  reflected  in  a  horizontal  direction  to  the  right  or  left,  it  is 
said  to  be  polarized  in  a  vertical  plane,  or  the  plane  of  polari- 
zation is  said  to  be  vertical.     If  it  could  be  reflected  vertically 
but  not  horizontally,  the  plane  of  polarization  would  then  be 
said  to  be  horizontal.     When  a  ray  is  polarized  by  reflection, 
the  plane  of  polarization  is  always  perpendicular  to  the  reflect- 
ing surface.    The  second  plate,  therefore,  is  capable  of  reflect- 
ing the  polarized  ray  in  its  plane  of  polarization,  but  will  not 
reflect  it  in  a  plane  perpendicular  to  the  plane  of  polarization. 

412.  It  is  to  be  particularly  observed  that  in  order  to  exhibit 
these  phenomena  in  the  best  manner,  the  ray  of  light  must 
make  the  proper  angle  of  incidence,  which  is  about  56°,  with 
both  of  the  glass  plates.     If  the  angle  of  incidence  at  the  first 
plate  varies  a  little  from  56°,  the  ray  will  not  be  completely 
polarized,  and  a  portion  of  the  light  will  therefore  be  reflected 
from  the  second  plate ;  and  if  it  makes  the  proper  angle  with 

Quest.  409.  May  the  beam  of  light  be  reflected  in  every  direction  by 
means  of  a  piece  of  painted  glass  ?  Does  it  possess  the  same  properties  on 
all  its  sides?  410.  If,  after  the  ray  enters  the  room,  it  is  reflected  at  the  pro- 
per angle  from  the  surface  of  a  piece  of  glass  laid  horizontally  upon  a  table, 
and  an  attempt  be  made  to  reflect  it  a  second  time  by  a  piece  of  glass,  what 
will  be  the  result  ?  In  what  directions  may  it  now  be  reflected  ?  and  in  what 
directions  does  it  refuse  to  be  reflected  ?  411.  When  is  a  ray  of  light  said  to 
be  polarized  in  a  vertical  plane  ?  When  is  the  plane  of  polarization  said  to 
be  horizontal  ?  When  a  ray  of  light  is  polarized  by  reflection,  what  is  the 
position  of  the  plane  of  polarization  with  reference  to  the  reflecting  surface  ? 
Will  the  second  glass  plate  reflect  the  polarized  ray  in  the  plane  of  polariza- 
tion ?  412.  What  is  the  angle  of  complete  polarization  ?  What  will  be  the 
effect  if  the  ray  does  not  make  exactly  the  proper  angle  with  either  the  first 
or  second  plate  ? 


OPTICS.  211 

the  first  plate,  but  not  with  the  second,  the  same  result  will  be 
obtained. 

413.  As  it  is  often  inconvenient  to  obtain  a  direct  ray  from 
the  sun  in  a  darkened  room,  a  lighted  candle  may  be  used  for 
the  experiment  with  good  success. 

Let  AB,  figure  196,  be  a 
plate  of  painted  glass  placed 

\  ^^4I>   upon  a  table,  and  C,  a  lighted 

candle   at  such  a  distance 
from  it  that  the  light  from 
••„  the  blaze  shall  make  with 

the  centre  of  the  plate  the 
Fig.  196.  proper  angle   of  incidence 

56°.  Then  let  a  person  station  himself  with  his  eye  at  E,  so 
as  to  see  the  image  of  the  candle  in  the  plate,  A  B;  and  taking 
a  second  plate  of  painted  glass  in  his  right  hand,  let  him  hold 
it  against  the  right  side  of  his  face  so  as  to  see  in  it  the  image 
of  the  candle  reflected  from  the  first  plate;  and  then,  carefully 
keeping  his  eye  upon  it,  let  him  turn  his  whole  body  gradually 
to  the  right.  The  plate  upon  the  table  and  the  image  of  the 
candle  in  it  will  seem  also  to  be  carried  round  as  he  turns ; 
and  if  he  has  been  successful  in  causing  the  light  to  make  the 
proper  angle  with  the  plates,  the  image  will  become  more  and 
more  faint  as  he  turns,  until  at  length  it  will  nearly  disappear. 
By  turning  himself  back  again,  the  image  is  made  gradually  to 
resume  its  former  brilliancy.  There  will  be  a  little  difficulty  at 
first  in  performing  the  experiment,  but  a  few  persevering  at- 
tempts will  insure  success.  It  will  be  found  that  the  image  of 
the  candle  is  faintest  when  the  second  plate  is  in  a  particular 
position,  and  becomes  brighter  whenever  this  position  is 
changed  in  any  direction. 

If  painted  glass  cannot  be  conveniently  obtained,  .the  experi- 
ment will  succeed  very  well  if  only  a  piece  of  black  cloth,  or  a 
black  glove,  is  laid  under  the  first  plate  of  glass,  and  another 
piece  is  held  against  the  back  of  the  second  plate.  The  results 
of  the  experiment  will  also  be  more  satisfactory  if  several  plates 
of  glass  are  placed  upon  each  other  on  the  table,  the  under  side 
of  the  lower  one  only  being  painted.  The  light  reflected  to  the 
second  plate  will  be  much  stronger  than  if  a  single  plate  only 
is  used. 

414.  Another  method  of  performing  the  experiment  is  to 
place  the  first  plate  of  glass,  A  B,  upon  a  table  standing  in  front 
of  a  window,  so  that  the  reflection  of  the  sky  may  be  seen  in  it 
at  the  proper  angle ;  and  then  taking  a  second  plate,  and  hold- 

Quest.  413.  How  may  the  experiment  of  polarizing  light  be  performed  by 
peans  of  a  candle  ?  Is  it  essential  to  have  the  pieces  of  glass  painted  ?  Will 
it  be  advantageous  to  use  several  polarizing  plates  instead  of  a  single  one  ? 
414.  How  may  the  experiment  be  performed  by  means  of  light  from  the 
sky? 


212  NATURAL     PHILOSOPHY. 

ing  it,  as  described  above,  so  as  to  see  in  it  the  reflection  of  the 
sky  from  the  first  plate,  and  turning  the  body  as  before.  As 
the  body  is  turned,  the  white  light,  at  first  reflected,  gradually 
vanishes,  until  at  length  the  plate  appears  nearly  black.  The 
sky-light  being  polarized  by  its  reflection  from  the  first  plate, 
refuses  to  be  reflected  from  the  second  when  the  proper  angle 
is  attained,  and  becomes  Jess  and  less  brilliant  as  this  angle  is 
approximated.  In  rough  experiments  like  these,  therefore,  it 
is  not  to  be  expected  that  results  as  satisfactory  can  be  obtain- 
ed as  by  the  use  of  apparatus  constructed  for  the  purpose,  with 
all  the  necessary  adjustments  for  obtaining  the  proper  angles. 


R 

Fig.  197. 

415.  The  principal  parts  of  a  piece  of  apparatus,  called  a 
polariscope,  used  for  polarizing  light  by  reflection,  is  repre- 
sented in  figure  197.  CD  is  a  tube  about  2  inches  in  diameter, 
usually  made  of  brass,  and  D  G  a  smaller  tube  of  the  same 
material,  made  so  as  to  slide  in  the  former.  A  and  B  are  plates 
of  painted  glass  fixed  to  their  supports  in  such  a  manner  that 
the  ray  rs  shall  make  the  proper  angle  of  56°  with  both  of 
them.  Let  the  apparatus  be  now  placed  on  a  proper  support 
near  a  window,  so  that  a  ray  of  light,  R  r,  from  the  sky,  may 
fall  upon  it,  and  be  reflected  through  the  tube  to  the  second 
plate,  B.  Since  the  tube,  DG,  can  be'made  to  turn  in  the  larger 
tube,  C  D,  which  is  supposed  to  be  fixed,  there  will  be  no  diffi- 
culty, as  there  was  before,  in  putting  the  plates  in  the  proper 
position  with  reference  to  each  other. 

Let  a  ray  of  light,  R  r,  from  the  sky,  or  from  a  lighted  candle, 
be  received  upon  the  plate,  A,  so  as  to  be  reflected  at  the  pro- 
per angle  through  the  .tubes  to  the  plate,  B,  and  let  the  tube, 
D  G,  be  gradually  turned  round  in  the  larger  tube,  C  D,  the  eye 
being  all  the  time  kept  at  E.  When  the  plates,  A  and  B,  are 
in  the  position  indicated  in  the  figure ;  that  is,  when  the  plane, 
rsE,  is  perpendicular  to  the  plane,  Rrs — the  plane  of  polari- 
zation (§41 1) — but  a  very  faint  light  will  be  perceived ;  but  as  the 
tube,  C  D,  is  turned  in  either  direction,  the  light  will  increase, 
and  will  be  brightest  when  it  has  made  a  quarter  of  a  revolu- 

Quest.  415.  What  are  some  of  the  principal  parts  of  the  apparatus  for 
polarizing  light  represented  in  figure  197  ? 


OPTICS.  213 

tion.  The  planes,  Rrs,  and  rsE, it  will  be  perceived,  will  then 
correspond,  in  whichever  direction  the  tube,  DG,  has  been 
turned.  But  if  the  tube  is  turned  still  further,  the  light  again 
becomes  fainter,  and  nearly  disappears,  when  another  quarter 
of  a  revolution  has  been  made,  bringing  the  two  planes,  Rrs, 
and  r  s  E,  again  perpendicular  to  each  other.  By  turning  through 
another  half  of  a  revolution,  the  same  changes  will  be  again 
observed  as  have  just  been  produced. 

416.  In  all  these  experiments,  the  action  of  the  first  or  polar- 
izing plate  seems  to  be  to  divide,  or  decompose,  the  light  into 
two  parts,  one  of  which  is  reflected  from  its  surface  to  the  se- 
cond plate,  while  the  other  passes  through  it  and  is  absorbed 
by  the  black  paint  or  cloth  on  the  other  side. 

417.  Though  we  have  thus  far  made  use  of  the  angle  of  56°  as  the  pro- 
per angle  of  incidence  for  polarizing  light  by  reflection  from  glass,  it 
should  be  remarked  that  the  more  correct  angle  is  56|  degrees.     Light  is 
also  polarized  by  reflection  from  the  surfaces  of  other  bodies  ;  but,  to  under- 
go this  change,  it  must  be  incident  upon  them  at  different  angles.     Thus, 
for  water,  the  proper  polarizing  angle  is  a  little  more  than  53°,  for  sul- 
phur, nearly  64°,  and  for  the  diamond,  68°.    When  light  is  incident  upon 
these  substances  at  angles  varying  a  little  from  the  above,  it  is  still  polar- 
ized,  but  the  polarization  is  not  complete. 

418.  Polarization  of  Light  by  Double  Refraction.  —  Long  be- 
fore anything  was  known  of  the  polarization  of  light,  it  was 
discovered  that  certain  transparent   substances  possess  the 
property  of  dividing  a  ray  of  light  transmitted  through  them 
into  two  parts,  and.  causing  small  objects  seen  through  them  to 
appear  double.     This  property  belongs  more  particularly  to 
crystallized  bodies,  as  Iceland  spar  (crystallized  carbonate  of 
lime),  quartz,  &c. ;  but  is  also  possessed  by  other  bodies,  as 
glass,  in  certain  circumstances. 

R  Let  A  C  B  D  F  G  H  M,  figure  198,  be  a  crystal 

of  Iceland  spar,  and  R  S  a  ray  of  light  falling 
perpendicularly  upon  it  at  S;  as  it  passes 
through  the  crystal  it  will  be  divided  into  two 
parts,  S  O,  and  S  E,  the  part  S  O  passing  di- 
rectly through  it,  as  it  would  through  glass  or 
water  without  refraction  (§  360) ;  but  the  other, 
S  E,  being  bent  considerably  out  of  the  origi- 
nal direction.  The  ray,  S  O,  is  called  the  or- 
dinary, and  S  E,  the  extraordinary  ray. 

419.  If  a  piece  of  white  paper,  with  a  dot 
upon  it  at  O,  is  laid  under  the  crystal,  there 

Quest.  416.  In  all  these  experiments,  what  is  the  action  of  the  first  or 
polarizing  plate  ?  417.  Is  the  angle  of  complete  polarization  for  all  sub- 
stances  the  same?  418.  What  peculiar  property  have  certain  transparent 
substances  been  long  known  to  possess  with  regard  to  a  ray  of  light  trans- 
mitted through  them  ?  To  what  bodies  does  this  property  more  particularly 
belong  ?  Is  it  possessed  by  other  bodies  also  to  some  extent  ?  What  aro 
the  two  rays  called  ?  419.  If  a  crystal  of  Iceland  spar  is  laid  upon  a  piece 


°\ 


214  NATURAL     PHILOSOPHY. 

will  appear  to  be  two  dots,  one  at  O  and  the  other  at  E.  If  the 
crystal  is  gradually  turned  round  on  the  paper,  the  dot,  E,  will 
appear  to  revolve  around  O,  keeping  always  on  the  same  side 
of  it,  with  reference  to  the  axis  of  the  crystal.  A  line  drawn 
upon  the  paper  in  the  direction  G  M,  when  observed  through 
the  crystal,  will  also  appear  double,  a  second  line  being  seen 
passing  through  E,  parallel  to  the  first ;  but,  if  the  crystal  is 
turned  round,  this  second  line  appears  to  approach  the  first, 
and  at  length  perfectly  coincides  with  it  when  the  crystal  has 
made  a  quarter  of  a  revolution.  If  the  crystal  is  turned  still 
further,  the  line  makes  its  appearance  on  the  other  side  of  O, 
and  attains  its  greatest  distance  from  O  when  the  crystal  has 
made  just  half  a  revolution.  When  the  crystal  has  made  three 
quarters  of  a  revolution,  the  lines  will  again  coincide;  and  if  it 
is  turned  still  further,  the  second  line  again  makes  its  appear- 
ance on  the  same  side  of  O  as  at  first,  both  lines  taking  the 
same  position  they  had  at  the  beginning  when  the  crystal  has 
made  a  full  revolution. 

420.  We  have,  in  the  above  experiments,  supposed  the  ray 
of  light  to  be  perpendicular  to  the  crystal,  and  we  find  the  or- 
dinary ray  passes  directly  through  without  refraction,  while 
the  other,  the  extraordinary  ray,  is  refracted.  If  the  ray  of 
common  light  is  made  to  strike  the  crystal  obliquely,  it  will 
still  be  separated  into  two  parts,  as  before,  and  the  ordinary 
ray  will  be  refracted  according  to  the  law  of  refraction  already 
described  (§  360),  but  the  extraordinary  will  deviate  entirely 
from  it. 

421.  In  every  body  capable  of  double 
refraction,  there  is  at  least  one  direction 
through  which  a  ray  of  light  will  pass 
without  suffering  this  change.  This  is 
called  its  optical  axis,  or  axis  of  double 
refraction.  In  Iceland  spar,  whose  pri- 
mary form  is  a  rhomb  (sometimes  called  a 
Fj  rhombohedron),  this  axis  is  in  the  direc- 

tion of  a  line  which  joins  its  two  obtuse 
solid  angles,  &c.,  AX,  figure  199.  So  this  axis  in  the  preceding 
figure  would  be  a  line  drawn  in  the  direction  AH.  A  section 
made  through  the  optical  axis  and  two  opposite  edges  of  the 
crystal,  as  ABFH,  figure  198,  is  called  its  principal  section. 

of  white  paper  marked  with  a  dot,  what  will  be  the  effect  ?  What  will  be 
the  effect  if  the  crystal  is  turned  round  ?  What  will  be  the  result  when  a 
line  is  drawn  upon  the  paper  and  the  crystal  turned  round  upon  it  ?  420.  If 
the  ray  of  light  is  incident  upon  the  crystal  obliquely,  will  double  refraction 
still  take  place?  421.  Does  double  refraction  take  place  whatever  may  be 
the  direction  of  the  ray  through  it  ?  What  is  meant  by  the  optical  axis  of  a 
crystal  ?  In  the  crystals  of  Iceland  spar,  in  what  direction  is  the  optical 
axis  ?  What  is  the  principal  section  ? 


OPTICS.  215 

422.  The  crystals  of  different  substances  exhibit  this  remark- 
able difference  in  their  action  upon  light,  that  in  some  the  ex- 
traordinary ray  SE,  figure  198,  is  bent  from  the  axis,  while  in 
others  it  is  bent  towards  it.    In  crystals  of  Iceland  spar  this  ray 
is  bent  from  the  axis  A  H ;  that  is,  it  deviates  more  from  being 
parallel  with  the  axis  than  the  ordinary  ray,  S  O.     In  crystals 
of  some  other  substances,  as  just  intimated,  the  extraordinary 
ray,  S  E,  will  be  refracted  towards  the  axis,  or  will  be  found 
on  the  other  side  of  S  O,  towards  H,  and  it  will  then,  it  is  evi- 
dent, be  more  nearly  parallel  with  the  axis  than  the  ordinary 
ray.     When  the  extraordinary  ray  is  refracted  from  the  axis, 
the  crystal  is  said  to  have  a  negative  axis ;  but,  when  it  is  re- 
fracted towards  the  axis,  it  is  said  to  have  a  positive  axis. 

In  crystals  of  many  substances,  there  are  two  or  even  a 
greater  number* of  axes  of  double  refraction ;  but  the  subject 
then  becomes  too  complex  to  be  here  discussed. 

423.  A  ray  of  light,  then,  on  passing  through  a  double  re- 
fracting substance,  is  separated  into  two  distinct  parts,  which 
take  entirely  different  courses  through  it.     But  the  separation 
of  the  rays  is  not  the  only  effect  produced  by  the  doubly  re- 
fracting substance.   If  the  rays,  after  separation,  are  examined, 
they  are  both  found  to  be  polarized  with  their  planes  of  polari- 
zation at  right  angles  to  each  other;  that  is,  if  the  two  rays, 
which  we  will  suppose  to  be  horizontal,  are  separately  made 
to  fall  upon  a  piece  of  painted  glass  at  the  proper  angle  of  inci- 
dence (56°),  they  will  both  exhibit  the  same  peculiarities  as  a 
ray  polarized  by  reflection  (§  410) ;  but,  if  one  of  them  may  be 
capable  of  reflection  upward  and  downward,  while  it  refuses 
to  be  reflected  to  the  right  or  left,  then  the  other  will  allow 
itself  to  be  reflected  to  the  right  or  left,  while  it  refuses  to  be 
reflected  vertically.     The  ordinary  ray  is  always  polarized  in 
a  plane  corresponding  to  the  principal  section,  and  the  extra- 
ordinary ray  in  a  plane  at  right  angles  to  this.    Consequently, 
if  we  suppose  the  experiment  made  by  placing  a  doubly  re- 
fracting crystal,  with  its  principal  section  vertical,  in  a  small 
aperture  made  for  the  purpose  in  the  window-shutter  of  a 
darkened  room,  through  which  a  direct  ray  from  the  sun  may- 
be received,  then  the  ordinary  ray  will  not  be  reflected  hori- 
zontally by  a  glass  plate,  nor  the  extraordinary  ray  vertically, 
while  the  former  will  allow  itself  to  be  reflected  vertically,  and 
the  extraordinary  ray  horizontally. 

Quest.  422.  What  difference  is  there  in  the  crystals  of  different  substances 
in  reference  to  the  direction  in  which  the  extraordinary  ray  is  refracted  ?  Is 
there  ever  more  than  one  axis  of  double  refraction?  423.  If  the  two  rays 
are  examined  after  passing  the  crystal,  in  what  respects  will  they  be  found 
to  differ  from  each  other  as  it  regards  their  planes  of  polarization  ?  If  a  ray 
of  light  is  received  through  a  crystal  placed  in  a  hole  in  the  window-shutter 
with  its  principal  section  vertical,  in  what  directions  may  the  ordinary  ray 
be  reflected  ?  and  in  what  directions  the  extraordinary  ray  ? 


216  NATURAL     PHILOSOPHY. 

424.  We  may,  therefore,  consider  a  ray  of  common  light  as 
made  up  of  two  separate  rays  which  are  polarized  in  opposite 
planes ;  that  is,  in  planes  which  are  at  right  angles  to  each 
other.     The  double  refraction  of  light  is,  therefore,  a  species 
of  decomposition  (§  379),  by  which  it  is  separated  into  two  dis- 
tinct rays,  which  are  not  indeed  of  different  colours,  as  in  the 
case  of  its  decomposition  by  means  of  the  prism,  but  which, 
nevertheless,  as  we  have  seen,  are  entirely  different  in  some 
of  their  properties. 

425.  When  light  is  polarized  by  reflection,  as  above  de- 
scribed (§410),  the  same' decomposition  takes  place,  though 
the  results  are  a  little  different.     When  light  is  polarized  by 
double  refraction,  both  rays,  after  separation,  pass  onward  in 
their  course,  though  in  directions  a  little  different ;  but  when 
it  is  polarized  by  reflection,  one  only  is  reflected  to  the  eye, 
while  the  other,  as  before  remarked,  passes  through  the  plate 
of  glass,  and  is  absorbed  by  the  black  paint  or  other  substance 
on  the  opposite  side  (§  416).     This  is  proved  by  using  a  plate 
of  glass  unpainted,  and  examining  the  ray  which  is  transmitted 
by  it.     This  ray  is  thus  found  to  be  polarized  equally  with  the 
reflected  ray,  but  in  a  plane  at  right  angles  to  the  plane  of 
polarization  of  the  reflected  ray. 

426.  Polarization  of  Light  by  Absorption.  —  Polarized  light 
may  also  be  obtained  by  simply  transmitting  a  ray  of  common 
light  through  thin  plates  of  certain  substances,  as  brown  tour- 
maline, and  agate,  when  cut  and  polished  in  the  proper  direc- 
tions.    In  this  case,  the  ray  of  common  light  is  decomposed 
into  two  rays  polarized  in  opposite  planes,  as  before,  and  one 
of  them  is  transmitted  while  the  other  is  absorbed  or  stifled  by 
the  polarizing  substance. 

Tourmaline  crystals  are  usually  in  the  form  of  six-sided 
prisms,  the  optical  axis  of  which  corresponds  with  the  axis  of 
the  crystal ;  and  pieces  prepared  for  polarizing  light  are  thin 
slips  cut  parallel  to  the  axis,  and  polished.  If  we  look  at  the 
sky  through  such  a  piece,  a  distinct  yellow  light  is  seen,  which 
is  scarcely  diminished  by  placing  a  second  piece  of  tourmaline 
on  the  first,  provided  the  two  are  parallel  with  their  lengths  in 
the  same  direction.  But  if  now  one  of  the  pieces  be  slowly 
turned  round  upon  the  other,  the  quantity  of  light  transmitted 
to  the  eye  will  gradually  diminish,  and  will  entirely  vanish 

Quest.  424.  Of  what  may  we  consider  the  common  ray  of  light  to  consist  ? 
Is  the  double  refraction  of  light  a  species  of  decomposition  ?  425.  Is  the 
same  decomposition  produced  when  light  is  polarized  by  reflection  ?  When 
light  is  polarized  by  reflection,  what  becomes  of  the  part  that  is  not  reflect- 
ed ?  How  is  this  proved  ?  426.  What  is  the  effect  when  a  ray  of  light  is 
transmitted  through  plates  of  tourmaline  or  agate  cut  in  the  proper  direction  ? 
How  are  the  two  rays  in  this  case  separated  From  each  other  ?  If  we  look 
at  the  sky  through  one  of  these  plates  of  tourmaline,  what  will  be  the  effect  ? 
If  two  plates  are  used,  and  one  is  made  to  turn  round  upon  the  other  as  the 


OPTICS.  217 

when  the  crystals  lie  across  each  other,  or  their  lengths  are  at 
right  angles.  If  it  be  turned  further,  the  light  again  appears. 

By  the  first  piece  of  crystal,  in  this  experiment,  the  ordinary 
or  common  ray  of  light  is  separated  into  two  rays  polarized 
in  planes  at  right  angles  to  each  other,  one  of  which  is  absorb- 
ed by  the  substance,  and  the  other  transmitted,  its  plane  of 
polarization  being  at  right  angles  to  the  axis  of  the  crystal. 
When,  therefore,  a  second  plate  of  tourmaline  is  presented, 
having  its  axis  in  a  plane  at  right  angles  to  the  axis  of  the  first, 
the  ray  refuses  to  pass. 

427.  Polarization  of  Light  by  Successive  Reflections.  —  Ano- 
ther method  still  of  polarizing  light  is  by  numerous  successive 
reflections  from  the  surface  of  glass  or  other  reflecting  sub- 
stance, at  an  angle  of  incidence  varying  more  or  less  from  the 
angle  of  complete  polarization.  Thus,  though  the  angle  of  com- 
plete polarization  for  glass  is,  as  above  stated,  56°,  yet  by  six 
successive  reflections  at  an  angle  of  70°,  a  ray  may  be  as  com- 
pletely polarized  as  by  a  single  reflection  at  an  angle  of  56°. 
So,  by  numerous  reflections  at  other  angles  greater  or  less 
than  56°,  the  same  effects  are  produced. 

428.  A  ray  of  common  light,  then,  being  considered  as  com- 
posed of  two  rays,  polarized  in  opposite  planes,  the  several 
methods  of  separating  these  rays,  and  obtaining  them  in  a 
state  of  separation,  are  the  four  following,  viz : 

1.  By  causing  the  ray  to  be  incident  upon  a  proper  reflecting 
surface,  as  that  of  glass  or  water,  at  its  angle  of  complete 
polarization  (§  410),  by  which  means  the  two  rays  of  which  it 
is  naturally  composed  are  separated,  one  being  reflected  from 
the  surface  polarized  in  the  plane  of  reflection,  and  the  other 
passing  through  the  glass  (§416),  and  emerging  polarized  in  a 
plane  perpendicular  to  the  first. 

2.  By  transmission  through  a  doubly  refracting  crystal,  by 
which  the  rays  are  separated  and  made  to  diverge  a  little  from 
each  other. 

3.  By  transmission  through  some  substance,  as  a  thin  plate 
of  brown  tourmaline  or  agate,  by  which  the  rays  are  separated 
as  before,  and  one  of  them  absorbed  or  stifled  by  the  polarizing 
body,  the  other  passing  through. 

4.  By  a  number  of  successive  reflections  from  the  surface 
of  some  transparent  substance  at  other  angles  than  that  of 
complete  polarization ;  by  which  means  it  is  supposed  the  planes 
of  polarization  are  turned  round  so  as  to  coincide  with  each 
other. 

eye  looks  through  them  to  the  clouds,  what  will  be  the  result  ?  How  is  this 
explained  ?  427.  May  light  be  polarized  by  numerous  successive  reflections 
at  any  angle  of  incidence  ?  428.  What  four  methods  of  polarizing  light 
have  we  ? 

19 


NATURAL     PHILOSOPHY. 

429.  Colours  produced  by  Polarization.  —  By  means  of  polar- 
ized light,  the  most  splendid  colours  may  be  produced,  of  sin- 
gular brilliancy.  To  exhibit  these  colours  to  the  best  advan- 
tage, a  nicely  constructed  apparatus  is  required,  like  that 
represented  in  figure  197,  with  the  addition  of  a  ring  between 
the  end  of  the  tube,  G,  and  the  plate,  B,  on  which  a  thin  plate 
of  selenite,*  or  mica,  maybe  placed,  in  such  a  manner  that  the 
ray  reflected  from  the  plate,  A,  may  pass  perpendicularly 
through  it. 


Fig.  200. 

In  order  to  exhibit  the  position  of  the  glass  plates  and  the 
plate  of  selenite  in  the  plainest  manner,  let  us  suppose  the  tube 
CG,  figure  197,  removed,  the  glass  plates,  A  and  B,  remaining 
in  the  same  position  as  before,  as  represented  in  figure  200,  and 
let  G  K  H  L  be  the  plate  of  selenite  or  mica.  This  should  be 
not  more  than  ^th  of  an  inch  in  thickness,  and  should  be  held 
so  that  the  rayVs  shall  pass  perpendicularly  through  it.  Let 
us  suppose,  also,  that  the  plate  of  selenite  is  held,  as  represented 
in  the  figure,  so  that  the  line  C  D  shall  be  in  the  plane  r  s  O; 
if  the  eye  be  now  placed  at  O,  nothing  but  the  dark  surface  of 
the  glass  will  be  seen  (§413),  the  plates  A  and  B  being  in  the 
position  in  which  the  light  that  is  reflected  polarized  from  the 
first  plate  A,  refuses  to  be  reflected  from  the  second  plate  B. 
But  if  the  plate  of  selenite  be  now  slowly  turned  round,  as  if 
on  the  line  r  s  as  an  axis,  it  will  appear  to  the  eye,  placed  at  C, 
to  be  covered  with  the  most  beautiful  tints,  which  become  more 
and  more  brilliant  until  the  line  G  H  comes  to  the  position  now 
occupied  by  C  D.  If  it  is  turned  still  further,  the  brilliancy  of 
the  colours  will  then  diminish  until  the  line  E  F  is  brought  to 
the  present  position  of  C  D,  when  they  will  entirely  vanish,  and 
only  the  dark  surface  of  the  glass  will  be  seen,  as  at  the  com- 
mencement. It  will  be  observed  that  the  plate  of  selenite  has 
now  made  just  a  quarter  of  a  revolution;  if  it  is  turned  still 
further,  the  same  appearances  will  present  themselves  as  be- 
fore, the  colours  alternately  appearing  and  disappearing  at 
each  quarter  of  a  revolution. 

Quest.  429.  What  is  said  of  the  colours  which  may  be  produced  by  polar^ 
ized  light  ?  What  substance  is  used  between  the  reflecting  plates  of  the 
polariscope  in  producing  these  colours  ?  What  will  be  the  effect  of  turning 
the  plate  of  selenite  round  as  described  ? 

*  Selenite  is  merely  crystallized  sulphate  of  lime  or  plaster  of  Paris.  It  is 
usually  in  thin  plates  which  are  easily  separated,  and  are  very  transparent. 
Mica  is  the  well-known  substance  used  int  the  windows  of  stoves.  It  is 
sometimes,  though  very  improperly,  called  isinglass. 


OPTICS. 

430.  It  is  found  that  the  particular  colours  that  are  produced 
depend  upon  the  thickness  of  the  plate  of  selenite ;  if  this  is  uni- 
form, the  colour  will  be  uniform  throughout;  but,  if  it  is  thicker 
at  some  places  than  at  others,  as  will  always  be  the  case  in  a 
piece  split  off  from  a  mass,  each  of  the  parts  of  different  thick- 
nesses will  have  a  tint  of  its  own.     If  the  plate  of  selenite  is 
inclined  a  little  to  the  ray  r  $,  a  different  tint  of  every  part  will 
be  produced,  as  the  ray  will  then  pass  through  a  greater  thick- 
ness of  it. 

431.  Let  us  now  suppose  we  have  a  plate  of  selenite  of  such 
a  thickness  as  to  give  a  uniform  red  colour,  and  let  us  suppose 
it  fixed  in  the  position  in  which  the  colour  is  brightest ;  this 
will  be  when  the  line  G  H  is  in  the  position  occupied  by  C  D  in 
the  figure  ($  429).     Let  the  plate  B  be  now  turned  round  in 
such  a  manner  that  it  shall  constantly  make  the  same  angle 
with  the  ray  rs;  when  it  begins  to  move,  the  brilliancy  of  the 
colour  will  instantly  begin  to  diminish,  and  will  entirely  disap- 
pear when  the  plate  B  has  made  |th  of  a  revolution,  or  has 
been  turned  through  45°.     If  it  is  turned  still  further,  the  plate 
of  selenite,  as  seen  by  reflection  from  B,  will  be  coloured  green, 
which  attains  its  greatest  brilliancy  when  the  plate  B  has  made 
another  eighth  of  a  revolution,  or  has  been  turned  a  quarter 
round  from  its  first  position.     If  the  plate  B  is  turned  still  ano- 
ther eighth  of  a  revolution,  the  green  gradually  becomes  fainter 
and  fainter,  and  at  length  vanishes ;  beyond  this  the  red  again 
appears,  and  attains  its  greatest  brilliancy  when  the  plate  B 
has  been  turned  half  round  from  its  position  at  the  beginning 
of  the  experiment.    By  turning  through  another  half  of  a  revo- 
lution the  same  changes  are  produced  as  have- just  been  de- 
scribed, and  in  the  same  order. 

432.  These  two  colours,  red  and  green,  are  said  to  be  com- 
plementary to  each  other,  because,  when  united,  they  produce 
white  light.     The  solar  spectrum  contains  the  three  rays,  red, 
yellow,  and  blue  ($  297),  which,  united,  produce  white;  but  the 
yellow  and  blue  united  produce  green;  therefore  the  red  and 
green  united  must  produce  white.    So  the  orange  and  the  blue 
united  produce  white,  and  are  therefore  complementary  to 
each  other.    In  the  above  experiment  the  colours  which  ap- 
pear as  the  plate,  B,  revolves  always  sustain  this  relation  to 
each  other;  if  one  is  red,  the  other  will  be  green;  if  one  is 

Quest.  430.  Upon  what  will  the  particular  colours  produced  depend  ?  What 
will  be  the  effect  if  the  plate  of  selenite  is  of  different  thicknesses  ?  What 
will  be  the  effect  if  the  plate  is  inclined  a  little  to  the  direction  of  the  polar- 
ized ray?  431.  If  the  plate  of  selenite  be  of  such  a  thickness,  and  in  the 
proper  position  to  produce  a  brilliant  red,  what  will  be  the  effect  if  the  se- 
cond plate,  B,  is  carefully  turned  round  in  the  manner  described?  How 
often  in  each  revolution  will  the  red  and  the  green  each  appear  and  disap- 
pear? 432.  Why  are  the  colours  red  and  green  said  to  be  complementary 
to  each  other  ?  Will  the  two  colours  which  appear  by  the  revolution  of  the 
plate,  B,  always  be  complementary  to  each  other? 


NATURAL     PHILOSOPHY. 

orange,  the  other  will  be  blue;  the  two  always  being  such  as, 
when  united,  to  produce  white. 

433.  If  the  student  finds  any  difficulty  in  understanding  the 
true  motion  which  is  to  be  given  to  the  plate,  B,  let  him  refer 
again  to  figure  197,  in  which  the  plates  are  represented  as  con- 
nected by  a  tube  composed  of  two  parts,  C  D  and  D  G,  the  lat- 
ter of  which  is  capable  of  turning  in  the  former.     The  motion 
supposed  to  be  given  to  the  plate,  B,  in  the  above  description, 
will  be  produced  simply  by  turning  the  part,  G,  to  which  the 
plate,  B,  is  attached,  in  the  part,  DC,  which  is  supposed  to  be 
fixed.     The  plate,  B,  while  the  tube  is  turned,  will  then  con- 
stantly make  the  same  angle  (56°)  with  the  polarized  ray,  r  s. 

434.  Some  of  the  important  results  of  the  above  experiment 
may  be  determined  merely  by  the  use  of  a  couple  of  pieces  of 
painted  window-glass,  as  described  above  (5  412),  and  a  small 
plate  of  selenite,  which  may  be  split  from  almost  any  crystal- 
lized specimen  of  sulphate  of  lime.   A  plate  of  mica,  of  the  pro- 
per thickness,  answers  the  same  purpose.   Let  a  piece  of  painted 
glass  be  placed  upon  a  table  near  a  window,  so  that  while  sky- 
light shall  be  reflected  from  it  to  the  eye  of  a  person  standing 
a  little  distance  from  it,  at  the  proper  angle  of  incidence  (56°) 
as  nearly  as  possible;  and  then,  as  before  (§  415),  let  him  hold 
a  second  piece  of  painted  glass  in  his  right  hand,  so  as  to  see 
in  it  the  light  reflected  from  the  first  plate.    By  turning  gradu- 
ally to  the  right,  the  brilliancy  of  the  light  will  diminish,  and 
when  the  proper  position  of  the  plates,  with  reference  to  each 
other,  is  obtained,  will  nearly  vanish,  the  surface  of  the  first 
plate  on  the  table  appearing  black,  as  seen  by  reflection  from 
the  second  plate.    If,  now,  the  plate  of  selenite  or  mica,  held  in 
the  left  hand,  is  interposed  between  the  glass  plates,  so  that 
the  light  reflected  from  the  first  shall  pass  perpendicularly 
through  it  on  its  passage  to  tfie  second  plate,  it  will  appear 
beautifully  coloured,  as  above  described,  the  particular  tints 
that  are  produced  depending  upon  the  various  circumstances 
above  enumerated  (§  431).   It  will  not  be  possible,  in  this  rough 
manner,  to  cause  any  colours,  as  the  red  and  green  (§  429),  to 
appear  and  disappear  regularly  by  turning  the  glass  plate  held 
in  the  hand ;  but  it  will  not  be  difficult,  by  turning  the  plate  of 
selenite  carefully  one  way  and  the  other,  to  find  that,  when 
held  in  two  positions,  with  reference  to  the  plane  of  reflec- 
tion of  the  second  glass,  no  colour  will  be  produced,  but  only 
the  dark  surface  of  the  first  plate  will  be  seen  through  the  sele- 
nite ;  in  all  other  positions  of  it,  the  colours  will  appear. 

Quest.  433.  How  may  some  of  the  important  results  above  detailed  be 
determined  merely  by  the  use  of  a  couple  of  pieces  of  painted  window-glass 
and  a  plate  of  selenite  or  mica  ?  Will  it  be  possible,  in  this  rough  manner, 
to  cause  the  complementary  colours,  as  red  and  green,  to  appear  regularly 
and  disappear  by  turning  round  the  plate,  B  ? 


OPTICS.  221 

435.  The  young  student,  in  attempting-  to  perform  this  experiment, 
will  find  the  greatest  difficulty  in  getting  the  proper  position  for  the  two 
glass  plates ;  but  he  may  always  know  when  the  object  is  accomplished, 
for  then  the  surface  of  the  first  plate  (the  one  placed  upon  the  table)  will 
appear  black  when  seen  by  reflection  from  the  second  plate.     The  diffi- 
culty in  a  particular  case  may  be  occasioned  by  the  light  not  being  re- 
flected from  the  first  plate  at  the  proper  angle  of  incidence  (56°),  or  by 
the  second  plate  not  being  held  in  the  proper  position  with  respect  to  the 
first.     Perfect  success  can  be  obtained  only  after  a  number  of  trials.     If 
the  first  trial  is  not  satisfactory,  and  it  is  suspected  that  the  light  is  not 
received  on  the  second  plate  at  the  proper  angle  of  reflection  from  the 
first  plate,  the  person  should  advance  a  little  nearer  to  the  table,  or  step 
back  a  little  farther  from  it,  as  he  may  judge  necessary,  by  which  the 
angle  of  reflection  will  be  changed.     But  care  should  always  be  taken 
that  the  white  light  of  the  sky  is  reflected  to  the  eye,  which  will  not  be 
the  case,  of  course,  if  the  shade  of  a  tree,  or  an  adjacent  building,  or  other 
object  is  seen  upon  the  glass  plate.     To  find  the  proper  position  of  the 
second  glass  plate  scarcely  any  directions  can  be  given  in  addition  to 
what  has  been  already  said  (§  414);  but  it  is  to  be  observed  that  very 
brilliant  colours  will  be  produced,  even  if  the  exact  angles  for  producing 
complete  polarization  are  not  obtained.     The  colours,  however,  appear 
much  the  most  beautiful  when  every  part  is  in  its  proper  position. 

436.  If,  instead  of  the  plate  of  selenite  or  mica,  in  the  above 
experiments,  a  crystal  of  Iceland  spar  be  used,  the  ray  passing 
through  it  in  the  direction  of  its  optical  axis,  brilliant  colours 
will  be  produced,  as  before,  but  they  will  be  arranged  in  con- 
centric circles.     To  prepare  a  crystal  for  this  purpose,  planes 
should  be  cut  and  polished  at  the  extremities  of  the  axis,  and 
perpendicular  to  it,  as  represented  in  figure  201. 

c A  ABXC  is  the  perfect  crystal,  and  the 

line  AX  its  optical  axis,  in  the  direction 
of  which  light  will  pass  without  undergo- 
ing double  refraction  (§  418).  The  parts 
at  the  extremities  of  the  axis,  AX,  repre- 
sented  by  dotted  lines,  are  to  be  ground 
Fig. 201.  down  and  polished;  and  a  ray  of  light 

incident  upon  one  of  these  faces  perpendicularly  will  then  pass 

directly  through  parallel  with  the  axis. 

437.  Having  the  glass  plates  in  the  proper  position  for  pro- 
ducing complete  polarization,  as  described  above — that  is, 
having  them  so  situated  that  the  first  plate  appears  black  when 
seen  by  reflection  from  the  first— let  the  prepared  crystal  of 
Iceland  spar  be  interposed  by  the  left  hand  between  them,  in 
the  same  manner  as  the  plate  of  selenite  ($  434),  and  it  will  be 
seen  covered  with  a  beautiful  system  of  coloured  rings,  inter- 

Quest.  436.  If,  instead  of  the  plate  of  selenite  or  mica,  as  described,  a 
crystal  of  Iceland  spar  be  used,  through  which  the  ray  is  made  to  pass  in 
the  direction  of  its  optical  axis,  what  will  be  the  result  ?  437.  If,  when  the 
two  plates  are  so  situated  as  to  produce  complete  polarization,  the  prepared 
crystal  of  selenite  be  introduced  between  them,  what  will  be  the  appearance  f 
19* 


222 


NATURAL     PHILOSOPHY. 


sected  by  a  black  cross,  as  repre- 
sented in  figure  202.  These  rings 
will  be  best  seen  when  the  plates 
are  held  as  near  together  as  possi- 
ble, with  the  eye  very  near  the 
second  plate. 

In  this  experiment  no  change  is 
produced  by  turning  round  the 
Iceland  spar,  but  if  the  second 
glass  plate  is  made  to  revolve  gra- 
dually, keeping  it  at  the  proper  an- 
gle to  the  polarized  ray,  the  rings 
will  be  found  to  vary  in  intensity ; 
and  when  a  quarter  of  a  revolution 
has  been  made,  an  entirely  new  system  of  rings  will  be  seen 
intersected  by  a  luminous  cross,  as  shown  in  figure  203. 


Fig.  202, 


Fig.  203. 


Fig.  204. 


438.  To  form  this  last  system  of  rings,  with  the  luminous 
cross,  in  a  familiar  way,  let  the  two  plates  of  painted  glass,  A 
and  B,  be  placed  as  in  figure  204,  and  let  P  be  the  prepared 
crystal  of  Iceland  spar.   The  plates  being  supposed  to  be  placed 
on  a  table  before  a  window,  a  ray  of  light,  R,  from  the  sky  is 
polarized  by  reflection  from  the  plate  A,  and,  after  passing 
through  the  crystal  of  Iceland  spar,  P,  is  reflected  by  the  se- 
cond plate,  B,  to  the  eye  at  E,  producing  the  system  of  coloured 
rings  just  described. 

The  system  of  rings  represented  in  figure  202,  with  the  dark 
cross,  may  also  be  formed  simply  by  turning  one  of  the  plates 
a  quarter  round,  so  that  their  planes  of  reflection  shall  be  at 
right  angles  to  each  other,  and  holding  the  prepared  crystal  of 
Iceland  spar  as  before. 

439.  These  experiments  are  more  easily  performed  by  using 
thin  plates  of  tourmaline  (§  423),  properly  prepared,  instead  of 
the  glass  plates,  but  it  is  difficult  to  procure  them.     The  same 
might  be  said  of  the  experiments  in  polarizing  light,  already 
described. 

Should  the  plates  be  held  near  each  other  in  performing  this  experiment  ? 
What  will  be  the  effect  if  the  plate  B  is  gradually  turned  round  ?  437.  May 
ihe  same  results  be  obtained  by  using  thin  plates  of  tourmaline  instead  of  the 


VISION.  223 

Crystals  of  substances  which  possess  two  axes  of  double 
refraction,  when  properly  cut  and  polished,  usually  produce 
two  systems  of  coloured  rings,  which  are  variously  situated 
with  respect  to  each  other,  according  to  their  structure  and 
the  position  of  their  axes. 


CHAPTER    VI. 
VISION. 

440.  THE  explanation  of  the  structure  of  the  eye,  and  the 
laws  of  vision,  forms  a  most  important  and  interesting  branch 
of  the  science  of  optics.    In  the  whole  range  of  natural  science 
there  is  not  to  be  found  a  more  beautiful  and  impressive  in- 
stance of  the  wonderful  skill  and  benevolence  of  the  Divine 
Architect  than  in  the  formation  of  the  eye,  and  its  adaptation 
to  the  purposes  for  which  it  is  designed. 

441.  The  human  eye,  except  a  small  portion  which  projects 
in  front,  is  of  a  very  perfect  spherical  form,  and  is  situated  in 
a  deep  cavity  in  the  bones  of  the  head,  which  is  called  its  orbit. 
It  is  thus  protected  from  mechanical  injuries,  to  which  it  would 
otherwise  be  constantly  liable.     As  it  is  situated,  only  a  very 
small,  or  a  pointed  object,  can  reach  it ;  and  but  a  small  part 
of  it  is  exposed  to  injury  even  from  such  objects.    Hence  it  is 
that  so  delicate  an  organ  is  preserved  in  perfect  order,  except 
the  slight  decay  of  age,  during  a  long  course  of  years,  in  the 
midst  of  the  numerous  accidents  to  which  every  one,  during 
life,  is  exposed. 

442.  The  different  parts  of  the 
eye  which  we  shall  notice  are  the 
thin  coats,  or  membranes,  which  are 
called  the  sclerotic  coat  (sometimes, 
also,  called  the  sclerotica),  the  cho- 
roid  coat,  and  the  retina;  the  two 
humours,  the  aqueous  and  the  vitre- 
ous ;  the  crystalline  lens  and  the  iris. 
Figure  205  is  a  front  view  of  the 
eye,  and  some  of  the  adjacent  parts. 
Fig.  205.  A  A  is  a  part  of  the  sclerotic  coatt 

reflecting  plates  of  glass  ?  Do  crystals  possessing  two  optical  axes  produce 
two  systems  of  coloured  rings  ?  440.  What  is  said  of  the  skill  and  benevo- 
lence of  the  Divine  Architect,  as  indicated  in  the  formation  of  the  eye,  and 
its  adaptation  to  the  purposes  designed  ?  441.  What  is  the  form  of  the  human 
eye  ?  Where  is  it  situated  ?  How  is  it  protected  from  mechanical  injury  ? 
442.  What  are  some  of  the  parts  of  the  eye  to  be  noticed  ?  What  is  the 


224  NATURAL    PHILOSOPHY. 

usually  called  the  white  of  the  eye,  being  always  of  a  beautiful 
white  colour;  II  is  the  iris,  so  called  from  the  circumstance  of 
its  presenting  so  many  different  shades  of  colour,  being  in 
some  persons  black,  in  others  blue  or  gray.  In  the  centre  of 
the  iris  is  a  small  circular  opening,  called  the  pupil,  varying 
from  one  to  two  or  three  tenths  of  an  inch  in  diameter,  ac- 
cording to  circumstances  to  be  hereafter  noticed.  Through 
this  small  aperture  all  the  light  enters  by  which  vision  is  pro- 
duced. 

443.  Figure  206  is  a  section  of 
the  left  eye  through  the  centre  of 
the  PUPH»  parallel  to  the  opening 
of  the  eye-lids,  the  lower  side  being 
supposed  next  to  the  nose.  ABBA 
is  the  sclerotica ;  it  is  a  strong  and 
tough  membrane,  perfectly  white, 
and  to  it  are  attached  the  several 
muscles  by  which  the  eye  is  moved 
in  its  socket,  so  as  to  enable  the 

person  to  see  in  different  directions  without  turning  the 
head.  A  A  is  the  cornea,  which  is  a  perfectly  transparent 
membrane  covering  the  front  of  the  eye,  and  connecting 
with  the  sclerotic  coat  all  around,  as  at  A  A.  It  receives 
its  name  from  its  resemblance  to  transparent  horn  (Latin 
cornu).  Next  inside  of  the  sclerotica  is  the  choroid  coat, 
indicated  by  a  darker  line;  it  is  a  delicate  membrane,  ex- 
tending from  the  optic  nerve,  O,  in  the  back  part  of  the  eye, 
to  the  iris,  II,  in  front,  with  which  it  is  connected.  On  its 
inside  it  is  covered  with  a  perfectly  black  substance,  called 
the  pigmentum  nigrum,  by  which  any  reflection  from  the  inter- 
nal parts  of  the  eye  is  prevented.  It  also  serves  to  absorb  any 
light  which  may  find  its  way  through  the  sclerotic  coat,  the 
two  producing  a  perfectly  darkened  chamber  within,  into  which 
light  is  admitted  only  through  the  pupil,  as  through  a  window. 
The  third  coat  is  the  retina,  RRR,  which  is  merely  an  expan- 
sion of  the  optic  nerve,  O,  and  lines  the  whole  of  the  back  part 
of  the  cavity  of  the  eye.  Upon  this  coat  a  perfect  image  is 
always  formed  of  every  object  seen  by  the  eye ;  and  the  pro- 
duction of  this  image  is  always  accompanied  by  the  sensation 
of  sight,  provided  the  optic  nerve,  which  connects  the  eye  with 
the  brain,  is  in  a  healthy  state.  This  nerve  enters  the  eye  in 

common  name  of  the  sclerotic  coat  ?  Where  is  the  iris  situated  ?  What  is 
the  pupil?  443.  What  is  represented  in  figure  206  ?  What  is  the  sclerotic 
coat  composed  of?  Where  is  the  cornea  ?  From  what  does  it  derive  its 
name  ?  Where  is  the  choroid  coat  ?  With  what  is  it  covered  on  the  inside  ? 
What  purpose  is  served  by  this  black  substance  ?  Where  is  the  retina  situ- 
ated? What  is  it?  What  is  always  formed  on  the  retina  when  perfect 
vision  takes  place  ?  Is  the  formation  of  the  image  upon  the  retina  always 
attended  by  the  sensation  of  sight  when  the  optic  nerve  is  in  a  healthy  state  ? 


VISION. 


225 


Fig.  207. 


the  back  part,  about  one-tenth  of  an  inch  from  the  axis,  on  the 
in-side,  towards  the  nose. 

The  crystalline  lens,  L,  is  a  compact,  transparent  substance, 
in  the  form  of  a  double  convex  lens,  but  having  one  surface 
more  convex  than  the  other;  in  connection  with  the  iris,  II,  it 
divides  the  eye  into  two  very  unequal  parts,  called  the  anterior 
and  posterior  chambers.  The  anterior  or  frontal  chamber  is 
filled  with  a  limpid  liquor,  like  water,  called  the  aqueous  humour; 
and  the  dense  vitreous  humour  fills  the  posterior  chamber. 

An  imaginary  straight  line,  C  D,  drawn  perpendicularly 
through  the  pupil,  is  called  the  axis  of  the  eye.  The  distance 
on  this  line  from  the  cornea  to  the  back  part  of  the  eye  is  gene- 
rally a  little  less  than  an  inch. 

In  front  of  the  whole  eye  is  the  con- 
junctiva, which  is  a  transparent  mem- 
brane designed  to  protect  the  eye  from 
the  entrance  of  dust  and  other  matter 
between  the  eye  and  its  socket.  It 
consists  merely  of  the  common  skin 
of  the  eye-lids,  A  and  B,  figure  207, 
above  and  below  the  eye,  which,  after 
passing  the  edges  of  the  lids,  folds  in 
a  little  distance,  and  is  reflected  over 
the  surface  of  the  cornea.  Foreign  matter,  therefore,  which 
enters  around  the  eye  can  never  find  its  way  farther  than  the 
fold  of  this  membrane  extends;  which,  however,  we  know 
often  causes  great  pain. 

444.  Let  us  now  inquire  concerning  the  effect  of  these  differ- 
ent parts  of  the  eye  in  producing  vision.  It  is  to  be  recollected 
that  every  point  of  a  visible  object  ($  336)  is  constantly  emit- 
ting rays  of  light  in  every  direction  ;  and  to  see  an  object  is  to 
see  the  points  of  which  its  surface,  presented  towards  the  eye, 
is  made  up,  arranged  in  their  proper  order  (§  351).  Of  the  rays 
emitted  from  any  point  only  a  small  portion  can  enter  the  eye,  so 
that  the  same  point  may  be  seen  at  the  same  time  by  many  eyes 
situated  in  the  vici- 
nity of  each  other, 
though  not  by 
means  of  the  same 
rays.  Let  ABC, 
figure  208,  be  an 
object  in  front  of 
an  eye;  of  the  rays 
emitted  from  the 

Where  does  the  optic  nerve  enter  the  eye  ?  What  is  the  form  of  the  crys- 
talline lens  ?  What  are  meant  by  the  anterior  and  posterior  chambers  of  the 
eye  ?  What  humour  fills  the  anterior  chamber  ?  What  fills  the  posterior 
chamber  ?  What  is  the  axis  of  the  eye  ?  What  is  the  conjunctiva  ?  What 
does  it  consist  of?  444.  What  is  it  to  see  an  object  ?  Will  all  the  rays  from 


226 


NATURAL     PHILOSOPHY. 


point  A,  a  small  portion  will  enter  the  pupil,  but  all  the  rays  in 
the  vicinity  which  come  in  contact  with  the  opake  parts  of  the 
eye  will  be  reflected  or  absorbed.  The  rays  that  enter  the  eye 
will  form  a  cone,  the  base  of  which  will  be  at  the  pupil,  and 
the  apex  at  the  point  from  which  they  are  emitted.  When 
these  rays  enter  the  cornea,  which  is  a  more  dense  medium 
than  the  air,  they  will  be  made  to  converge ;  and  this  effect 
will  be  still  further  increased  by  their  passing  through  the  crys- 
talline lens,  so  that  they  will  be  brought  to  a  focus  on  the  retina 
at  a,  producing  there  an  image  of  the  point  A  of  the  object 
from  which  they  were  first  emitted.  From  every  other  point 
of  the  object,  as  B  and  C,  cones  of  rays  will  proceed  in  like 
manner,  producing  at  b  and  c,  on  the  retina,  corresponding 
images  of  these  points.  The  result  of  the  whole  will,  therefore, 
be  the  production,  on  the  retina  in  the  back  part  of  the  eye,  of 
an  inverted  image,  a  b  c,  of  the  object  A  B  C  (§  374). 

Both  the  aqueous  and  vitreous  humours  have  some  effect  in 
bringing  the  rays  to  a  focus  on  the  retina  for  the  production 
of  the  image,  but  the  crystalline  lens  is  the  most  important. 
The  form  of  this,  as  we  have  seen,  is  double  convex,  the  con- 
vexity being  greatest  on  the  side  next  to  the  vitreous  humour, 
while  the  aqueous  humour  has  the  form  of  a  meniscus,  with 
its  convex  side  presented  to  the  rays,  and  the  vitreous  that  of 
a  convex  or  concave  lens  (§  369). 

445.  We  know,  merely  by  an  examination  of  the  different 
parts  of  the  eye,  that  when  an  object  is  placed  in  front  of  it,  an 
image  of  it  will  be  formed  on  the  retina 
in  the  back  part;  but  the  same  thing 
-can  be  shown  by  direct  experiment. 
For  this  purpose  the  eye  of  an  ox  or 
other  animal  which  has  been  recently 
killed  is  taken,  and  the  two  outer  coats 
carefully  removed  from  the  back  part, 
so  as  to  expose  the  semi-transparent 
reiina.  If,  when  thjis  prepared,  it  is 
held  before  a  window,  or  other  bright 
object,  the  inverted  image,  perfectly 
distinct,  will  be  seen  formed  upon  the 
retina.  As  this  membrane  is  semi- 


Fig.  209. 


each  point  of  an  object  enter  the  eye  ?  What  will  the  rays  that  enter  the 
eye  from  any  point  form  ?  What  effect  is  produced  upon  this  cone  of  rays 
from  any  point  where  they  enter  the  cornea  ?  What  will  be  the  effect  when 
they  pass  the  crystalline  lens  ?  Where  will  the  image  of  the  point  be  formed  ? 
Will  similar  images  of  other  points  be  formed  ?  What  will  the  result  of  the 
whole  be  ?  Do  the  vitreous  and  aqueous  humours  produce  any  effect  ?  On 
which  side  of  the  crystalline  lens  is  the  greatest  convexity  ?  What  is  the 
form  of  the  aqueous  humour?  Of  the  vitreous  humour?  445.  How  may 
the  eye  of  an  ox  or  other  animal  be  prepared,  so  as  to  exhibit  the  formation 
of  the  image  upon  the  retina  of  an  object  in  front  of  it  ?  What  is  shown  in 
figure  209  ? 


VISION.  227 

transparent,  the  image  formed  upon  it  is  seen  through  it.  Figure 
209  represents  an  eye  of  an  ox  prepared  in  this  manner,  and 
held  before  a  window,  the  inverted  image  of  which  is  seen  in 
the  back  part. 

446.  As  the  eye,  though  small,  is  capable  of  seeing  distinctly, 
at  a  single  view,  the  various  objects  of  an  extensive  landscape, 
it  is  evident  the  images  must  be  painted  on  the  retina  with 
wonderful  minuteness.     It  has  been  calculated  that  the  image 
of  a  portion  of  the  castle  of  Edinburgh,  500  feet  long  and  90 
feet  in  height,  when  seen  at  a  certain  distance,  does  not  occupy 
on  the  retina  more  than  the  twelve  hundred  thousandth  part 
of  an  inch,  and  yet  its  different  parts  will  be  distinctly  visible. 
When  a  page  of  a  large  book  is  held  before  the  eye,  not  only 
is  each  word  and  letter  distinctly  visible,  but  even  the  minute 
defects  of  the  letters;  and  yet  the  image  of  the  whole  upon  the 
retina  will  not  cover  a  space  so  large  as  the  finger-nail !    It  is 
not  necessary  to  remark  that  no  painter,  however  skilful  with 
the  pencil,  can  execute  a  picture  like  this. 

447.  It  is  well  known  that  the  eye  is  capable  of  viewing  ob- 
jects distinctly  at  greatly  different  distances  within  certain 
limits.     The  least  distance  of  distinct  vision  for  most  persons 
is  about  5  inches,  but  all  can  see  much  farther  than  this.     But, 
in  order  that  a  distinct  image  of  objects  at  different  distances 
may  be  produced,  it  is  absolutely  necessary  that  the  parts  of 
the  eye  should  undergo  some  change.     If  the  parts  of  the  eye 
were  incapable  of  change,  a  distinct  image  would  be  formed 
on  the  retina  only  when  objects  were  at  a  particular  distance, 
but  would  be  confused  if  the  objects  were  brought  nearer  or 
carried  farther  off.     To  be  satisfied  of  this,  let  a  person  hold  a 
common  burning-glass  a  few  feet  from  a  candle,  in  a  dark 
room,  as  described  above  (§  375),  and  at  a  certain  distance  on 
the  opposite  side  of  the  glass,  which  can  easily  be  found  by 
trial,  an  inverted  image  of  the  candle  will  be  formed  on  a  sheet 
of  paper  or  other  substance  held  up  as  a  screen  to  receive  it. 
If  the  candle  be  now  removed  a  little  farther  from  the  glass,  the 
image  at  once  becomes  indistinct,  but  is  again  perfectly  formed 
if  the  screen  is  brought  a  little  nearer ;  so  if  the  candle  is  placed 
nearer  to  the  glass  than  when  in  its  first  position,  the  image 
again  becomes  indistinct,  a  perfect  image  being  produced  only 
when  the  candle  and  paper  are  at  certain  relative  distances 
from  the  glass. 

Quest.  446.  What  is  said  of  the  minuteness  with  which  images  of  objects 
must  be  painted  upon  the  retina?  What  illustration  of  this  is  given  in  the 
instance  of  a  person  viewing  a  portion  of  the  castle  of  Edinburgh  at  a  cer- 
tain distance  ?  What  is  said  of  the  space  occupied  by  the  image  of  the  page 
of  a  book  at  which  a  person  is  looking.  447.  Is  the  eye  capable  of  seeing 
objects  distinctly  at  different  distances  from  it  ?  What  is  the  least  distance 
of  distinct  vision  for  most  persons  ?  Must  some  change  take  place  in  the 
parts  of  the  eye  when  objects  are  viewed  at  different  distances?  If  the  parts 
of  the  eye  were  incapable  of  change,  what  would  be  the  result  ?  By  what 


228  NATURAL     PHILOSOPHY. 

It  is  found  that  if  the  parts  of  the  eye  remain  unchanged,  the 
distance  of  the  image  from  the  crystalline  lens,  of  objects  situ- 
ated only  about  5  inches  (§  446)  from  the  eye,  will  be  about 
jth  of  the  diameter  of  the  eye  more  than  if  the  objects  are 
placed  at  the  greatest  distance  of  distinct  vision.  But  as  the 
image,  to  produce  distinct  vision,  must  always  be  thrown  ac- 
curately upon  the  retina,  to  enable  a  person  to  see  both  near 
and  distant  objects,  it  is  evident  the  parts  of  the  eye  must 
undergo  some  change ;  and  that  this  change  does  take  place 
every  one  will  be  satisfied  by  looking  attentively  for  some 
seconds  at  a  well-illuminated  distant  object,  and  suddenly  turn- 
ing his  eye  upon  the  page  of  a  book  held  in  his  hand.  For  a 
moment,  after  turning  his  eye  upon  the  book,  the  print  will  ap- 
pear more  or  less  blurred,  until  the  parts  of  the  eye  which  have 
been  adjusted  for  looking  at  the  distant  object  have  time  to  put 
themselves  in  the  proper  order  for  seeing  those  that  are  near. 

448.  There  are  three  modes  by  which  the  eye  may  adjust 
itself  for  seeing  objects  at  different  distances — that  is,  so  as  to 
cause  the  image  to  be  formed  on  the  retina,  though  the  dis- 
tance of  the  object  may  vary — viz :  1.  By  a  change  in  the  con- 
vexity of  the  cornea  and  crystalline  lens ;  or,  2.  By  a  change 
in  the  distance  of  the  crystalline  lens  from  the  retina;  or,  3. 
By  both  combined.     Thus,  if  the  parts  of  the  eye  are  adjusted 
for  seeing  near  objects,  to  enable  it  to  see  clearly  distant  ob- 
jects, it  is  necessary  only  that  the  cornea  and  crystalline  lens 
should  be  a  little  flattened,  to  prevent  the  rays  from  coming 
to  a  focus  before  reaching  the  retina ;  or,  that  the  crystalline 
lens  should  be  moved  forward  a  little  farther  from  the  retina ; 
or,  that  both  of  these  changes  should  take  place  together. 
Some  writers  have  affirmed,  without  qualification,  that  these 
changes  actually  take  place,  but  it  is  believed  no  sufficient 
evidence  of  them  has  yet  been  produced;  and  the  mode  by 
which  the  eye  adjusts  itself  to  see  objects  at  different  distances 
cannot  be  considered  as  fully  determined. 

449.  When  a  person  steps  suddenly  from  a  room  perfectly 
dark  into  one  well  lighted,  a  painful  sensation  is  produced  in 
the  eyes,  and  he  is  scarcely  able  to  see,  because  of  the  excess 
of  light ;  but  in  a  short  time  the  eye  accommodates  itself  to 
the  light,  and  the  pain  ceases.     So,  when  a  person   goes  at 
once  from  a  well-lighted  apartment  into  a  dark  room,  or  into 

simple  experiment  may  a  person  satisfy  himself  of  this  ?  If  an  object  is  only 
5  inches  from  the  eye,  how  much  farther  from  the  crystalline  lens  will  the 
image  be  formed  than  if  it  is  situated  at  the  greatest  distance  of  distinct 
vision  ?  How  may  a  person  satisfy  himself  that  the  ej'e  actually  undergoes 
a  change  when  he  looks  from  a  near  to  a  distant  object,  or  the  reverse  ? 
448.  What  three  modes  are  mentioned  by  which  the  eye  may  adjust  itself 
so  as  to  perceive  objects  at  different  distances  ?  Has  it  been  proved  that 
these  changes,  or  any  of  them,  do  actually  take  place?  449.  What  is  the 
effect  upon  the  eyes  when  a  person  steps  suddenly  from  a  dark  to  a  well- 
lighted  apartment  ?  What  is  the  effect  of  going  at  once  from  a  room  bril- 


VISION.  229 

the  open  air  on  a  dark  night,  he  is  at  first  scarcely  able  to  dis- 
tinguish a  single  object,  but  by  degrees  he  finds  his  vision 
become  much  more  distinct.  This,  it  is  well  ascertained,  is 
occasioned  by  the  contraction  and  expansion  of  the  iris,  by 
which  the  diameter  of  the  pupil  is  changed.  When  a  person 
views  a  well-illuminated  object,  the  diameter  of  the  pupil  is 
scarcely  TVth  of  an  inch,  and  but  a  small  pencil  of  rays  is  ad- 
mitted, which,  if  he  steps  into  a  room  only  partially  lighted, 
will  not  be  sufficient  to  produce  distinct  vision ;  but  the  iris 
spontaneously  dilates,  and  a  larger  pencil  of  rays  is  admitted, 
to  enable  him  to  see  distinctly.  After  remaining  a  while  where 
there  is  little  light  the  pupil  dilates  to  its  utmost  size,  and  if  he 
now  suddenly  step  into  a  well-lighted  room  so  much  light 
enters  the  eye  as  to  produce  pain,  but  the  gradual  contraction 
of  the  pupil  soon  causes  it  to  cease,  by  diminishing  the  quantity 
of  light  that  is  admitted.  Any  one  may  witness  this  change  in 
his  own  eyes  by  holding  a  small  mirror  in  his  hand,  and  so 
managing  as  to  look  suddenly  from  an  obscure  object  to  one 
that  is  well  illuminated,  or  the  reverse.  The  eyes  of  children 
are  especially  sensitive  to  light,  and  by  causing  a  child  to  look 
first  at  the  window,  when  the  sun  shines,  and  then  at  some 
object  in  the  room,  or  the  reverse,  the  change  in  the  size  of  the 
pupil  will  be  beautifully  exhibited. 

450.  Some  persons,  it  is  said,  have  the  power  of  enlarging 
or  contracting  the  pupil  of  the  eye  at  pleasure,  but  it  is  be- 
lieved this  is  seldom  the  case,  the  change  of  the  pupil  to  accom- 
modate the  eye  to  the  quantity  of  light  being  entirely  sponta- 
neous, and  beyond  the  control  of  the  will. 

451.  In  some  animals  the  pupil  of  the  eye  is  susceptible  of 
much  greater  change  than  in  man,  so  that  they  can  see  equally 
well  with  him  in  the  day- time,  and  much  better  in  the  night, 
when  objects  are  but  partially  illuminated.     This  is  the  case 
with  the  horse;  and  it  is  well  known  that  he  will  find  his  way 
along  in  a  dark  night,  when  it  would  be  absolutely  impossible 
for  a  man  to  do  it  alone.     This  is  also  particularly  observable 
in  animals  of  the  cat  kind,  which  are  adapted  for  searching  for 
their  prey  in  the  night.     Some  animals,  as  bats  and  certain 
species  of  owls,  cannot  see  well  in  the  day-time,  and  therefore 
seldom  appear  abroad  except  at  evening,  when  their  vision 
becomes  distinct ;  this  is  because  their  eyes  being  adapted  for 
seeing  clearly  only  at  night,  their  pupils  do  not  allow  of  suffi- 

liantly  illuminated  into  one  that  is  dark,  or  into  the  open  air  in  a  dark  night  ? 
How  are  these  facts  explained  ?  How  may  a  person  notice  this  change  in. 
his  own  eyes  ?  How  may  it  be  noticed  in  the  eyes  of  a  child  ?  450.  Have 
we  the  power  of  enlarging  or  contracting  the  pupils  of  our  eyes  at  pleasure  ? 
451.  Are  the  pupils  of  the  eyes  of  some  animals  susceptible  of  greater  change 
in  this  respect  than  those  of  man  ?  Can  such  animals  see  better  in  the  night, 
when  objects  are  but  partially  illuminated,  than  man  ?  In  what  animals  is 
this  particularly  observable  ?  Why  can  some  animals  see  better  in  the  twi- 
20 


230  NATURAL     PHILOSOPHY. 

cient  contraction  to  enable  them  to  see  in  the  broad  light  of 
day.  The  pupil  of  the  eye  in  man  is  always  round,  but  in 
some  animals,  as  the  horse,  it  is  elongated  in  a  horizontal  di- 
rection, while  in  others,  as  the  cat,  it  is  elongated  vertically. 
The  eyes  of  fishes  are  always  destitute  of  the  aqueous  humour, 
which,  as  they  are  designed  to  live  in  the  water,  would  be 
useless;  and  the  crystalline  lens  is  spherical.  This  is  rendered 
necessary  by  the  fact  that  the  rays  of  light  pass  from  a  dense 
medium,  water,  into  the  eye;  for,  if  the  crystalline  lens  was 
not  more  convex  than  in  the  eyes  of  land  animals,  the  rays 
would  not  be  soon  enough  brought  to  a  focus,  so  as  to  form 
an  image  upon  the  retina. 

452.  It  has  been  seen  above  (§  376)  that  when  rays  of  light 
which  are  parallel,  or  nearly  so,  are  transmitted  through  a 
double  convex  lens  of  glass,  they  are  not  all  brought  to  a  focus 
at  the  same  distance,  but  those  transmitted  near  the  edge  come 
to  a  focus  nearer  to  the  lens  than  those  which  pass  through 
near  its  centre.     This  is  avoided  in  the  eye  by  the  increased 
density  of  the  crystalline  lens  near  its  centre,  by  which  its 
refractive  power  in  this  part  is  increased.     Besides  this,  the 
iris  serves  as  a  diaphragm,  by  which  the  rays  too  distant  from 
the  axis  are  excluded.    The  eye,  therefore,  is  destitute  of  sphe- 
rical aberration. 

453.  It  has  been  seen,  likewise,  (5  378),  that  when  light  is 
refracted,  the  primary  colours  of  which  it  is  composed  are 
separated  more  or  less  from  each  other ;  so  that  when  a  pencil 
of  rays  is  transmitted  through  a  double  convex  lens,  the  image 
formed  will  usually  appear  coloured.     But  no  such  effect  is 
produced  by  the  eye,  which  sees  all  objects  of  their  natural 
colour.     In  the  small  pencil  of  light  admitted  into  the  eye,  only 
a  slight  dispersion  of  the  colours  can  take  place,  and  this,  it  is 
supposed,  is  corrected  by  the  different  dispersive  powers  (§  386) 
of  the  different  parts  of  the  eye. 

By  a  particular  experiment  the  colours  of  the  spectrum  may 
be  seen,  the  light  being  decomposed  by  the  eye.  Let  a  person 
hold  some  opake  object  with  a  straight  edge,  as  a  book,  be- 
tween his  eye  and  the  window,  parallel  with  one  of  the  cross- 
pieces  of  the  sash,  so  as  to  see  only  a  narrow  line  of  light,  and 
a  very  small  prismatic  spectrum  will  be  formed,  containing, 
according  to  Brewster,  all  the  different  colours. 

light  than  in  the  broad  light  of  day  ?  What  is  the  form  of  the  pupil  of  the 
eye  in  man  ?  Is  it  of  the  same  form  in  the  eyes  of  other  animals  ?  Why 
do  the  eyes  of  fishes  have  no  aqueous  humour  ?  What  is  the  form  of  the 
crystalline  lens  in  their  eyes  ?  452.  Will  all  the  rays  of  a  pencil  of  light, 
transmitted  through  a  double  convex  lens  of  glass,  be  brought  to  a  focus  at 
the  same  point  ?  How  is  this  avoided  in  the  eye  ?  What  purpose  does  the 
iris  serve  in  producing  the  same  result?  453.  Why  are  not  the  differently 
coloured  rays  separated  by  the  parts  of  the  eye  in  the  same  manner  as  when 
refracted  by  other  media  ?  How  may  it  be  shown  that  in  some  cases  the 
several  colours  are  separated  by  the  parts  of  the  ey«  ? 


VISION.  231 

454.  As  distinct  vision  is  produced  only  when  the  light  from 
objects  is  brought  to  a  focus  exactly  on  the  retina,  the  eyes  of 
persons  may  be  defective  by  having  too  great  refractive  power, 
so  as  to  cause  the  images  to  be  formed,  not  on  the  retina,  but 
a  little  in  front  of  it;  or  by  having  too  little  refractive  power, 
in  which  case  the  light  is  not  brought  to  a  focus  soon  enough, 
but  tends  to  form  the  image  a  distance  behind  the  retina. 

455.  The  first  defect  is  frequently  seen  in  young  persons,  and 
is  occasioned  by  too  great  a  convexity  of  the  cornea  or  crys- 
talline lens.     Such  persons  can  see  clearly  only  those  objects 
which  are  very  near  them,  and  are  therefore  said  to  be  near 
sighted.     To  enable  them  to  see  distant  objects,  it  is  necessary 
to  make  the  rays  diverge  a  little  before  entering  the  eye,  by 
which  means  the  image  will  be  thrown  back  a  little  to  the 
retina.    This  is  accomplished  by  the  use  of  spectacles  with  con- 
cave glasses,  the  effect 
of  which  is  to  separate 
the  rays.    Figure  210 

A  represents  an  eye  of 
"  this  kind ;  A,  a  small 
object  in  front  of  it, 
and  MN  a  double  con- 
cave lens,  to  disperse 
Pig.  210.  (§  373)  the  light  before 

entering  the  eye.  The  dotted  lines  show  the  direction  the  rays 
would  take  if  the  lens  was  not  interposed.  It  will  be  seen  they 
intersect  each  other  before  reaching  the  retina,  and  at  this  point, 
but  for  the  effect  of  the  lens,  the  image  would  be  formed  ;  but 
by  means  of  the  lens  to  separate  them  a  little,  the  image,  a,  is 
not  formed  until  they  reach  the  retina.  Persons  are  sometimes 
met  with,  one  of  whose  eyes  is  more  convex  than  the  other, 
which  is  a  defect  that  requires  the  use  of  spectacles  having  one 
lens  more  concave  than  the  other. 

456.  Near-sighted  persons,  who  can  see  distant  objects  only 
by  the  use  of  concave  glasses,  never  can  have  so  large  a  field 
of  view  as  is  afforded  by  the  unaided,  perfect  eye ;  their  glasses 
enable  them  to  see  clearly  only  those  objects  which  are  situ- 
ated in  a  small  circle  directly  before  them. 

457.  Most  persons,  on  attaining  the  age  of  about  forty-five, 
find  their  vision  becomes  indistinct  from  causes  directly  the 
reverse  of  those  described  above,  in  the  case  of  near-sighted- 

Quest.  454.  In  what  two  respects  mentioned  may  the  eyes  of  persons  be 
defective  ?  When  the  refractive  power  is  too  great,  where  is  the  image 
formed  ?  Where  when  the  refractive  power  is  too  small  ?  455.  In  whom 
is  the  first  defect  frequently  seen  ?  How  is  it  occasioned  ?  What  objects 
only  are  seen  clearly  by  such  persons  ?  What  is  necessary  to  enable  them 
to  see  clearly  ?  How  is  this  accomplished  ?  When  one  eye  of  a  person  is 
more  convex  than  the  other,  how  is  the  defect  remedied  ?  456.  Can  near- 
sighted persons  have  as  large  a  field  of  view  as  others  ?  457.  At  what  age 
does  the  vision  of  most  persons  become  indistinct  from  causes  the  reverse  of 


232  NATURAL     PHILOSOPHY. 

ness.  The  change  is  most  likely  to  be  first  observed  when 
they  attempt  to  read  very  fine  print,  or  to  examine  some  mi- 
nute object  by  candle-light.  Though  unable  to  see  clearly 
when  the  object  is  held  at  the  usual  distance  from  the  eye,  they 
soon  find  that  when  it  is  removed  a  little  farther  off,  the  dis- 
tinctness is  improved.  By  this  test  persons  may  alwa-ys  know 
when  this  change  is  beginning  to  take  place  in  their  eyes. 

458.  This  indistinctness  of  vision  in  aged  persons  is  occa- 
sioned by  the  flattening  which  takes  place  in  the  cornea  and 
crystalline  lens.     The  light  which  enters  the  eye  from  near 
objects  is  not  brought  to  a  focus  soon  enough,  but  tends  to 
form  the  image  a  little  beyond  the  retina.    This  defect  is  reme- 
died by  the  use  of  convex  glasses,  by  which  a  slight  con- 
vergency  is  given  to  the  rays  before  they  enter  the  eye.    Let 

A  B,  figure  211, 
be  an  eye,  the 
parts  of  which 
have     become 
thus    flattened 
by   age;    O   a 
small       object 
_______  placed     before 

it,  and  MN  a 
double  convex 

lens.  The  rays  of  light  diverge  from  the  object,  O,  and  after 
being  slightly  bent  inward  by  the  lens,  enter  the  eye,  by  which 
they'are  brought  to  a  focus  so  as  to  form  the  image  upon  the 
retina,  as  shown  by  the  dark  lines.  The  dotted  lines,  as  before, 
are  designed  to  show  the  course  the  rays  would  take  if  the 
glass  were  removed.  It  will  be  seen  that  without  the  lens  no 
image,  or  only  an  indistinct  one,  can  be  formed  upon  the  retina, 
the  focus  being  then  at  a  distance  beyond  it. 

459.  In  most  cases,  persons  whose  eyes  have  become  thus 
flattened  by  age  can  distinguish  distant  objects  with  as  much 
clearness  as  in  youth ;  or  it  is  only  in  extreme  old  age,  when 
the  eyes  have  become  much  flattened,  that  glasses  are  required 
for  this  purpose.     This  is  because  the  rays  from  distant  ob- 
jects are  less  diverging,  or  nearly  parallel  when  reaching  the 
eye,  so  that  the  convexity  of  the  parts  of  the  eye  is  still  suffi- 
cient to  bring  them  to  a  focus  at  the  proper  point.     Instances 
have  been  known  in  which  persons  whose  vision  has  been  long 
indistinct,  in  consequence  of  the  flattening  of  their  eyes,  have, 
in  extreme  old  age,  recovered  their  sight,  and  been  able  to 

those  described  above  ?  When  is  the  change  likely  to  bo  first  observed  by 
them?  How  is  their  vision  affected  by  moving  the  object  a  little  farther 
from  the  eye  ?  458.  By  what  is  this  indistinctness  of  vision  occasioned  ? 
Where  is  the  tendency  to  form  the  image  ?  How  is  this  defect  remedied  ? 
Can  a  distinct  image  be  formed  without  the  lens?  459.  Can  aged  persons 
usually  see  distant  objects  clearly  ?  How  is  this  explained  ?  Will  specta- 


VISION.  233 

read  even  the  smallest  print  without  the  use  of  spectacles ;  but, 
generally,  the  defect  continues  to  increase  with  age,  as  long 
as  the  person  lives.  Of  course,  spectacles  that  answer  well  at 
one  age  become  afterwards  useless,  and  require  to  be  changed 
for  others  that  are  more  convex.  Glasses  that  thus  become 
useless  are  sometimes  said  to  be  too  young  for  the  person ;  and 
if  he  can  see  with  them  at  all,  it  is  only  by  holding  the  object 
at  a  considerable  distance  from  him,  as  is  the  case  with  a  per- 
son (§  457)  who  has  just  arrived  at  the  age  when  his  natural 
vision  begins  to  become  indistinct. 

460.  Though  spectacles  are  now  found  so  important  for  aged 
persons,  and  are  universally  used,  it  is  scarcely  six  hundred 
years  since  they  were  invented.     We  know  from  many  pas- 
sages of  scripture  which  speak  of  the  eye's  becoming  dim  by 
age,  as  well  as  from  profane  history,  that  the  eyes  of  persons 
in  ancient  times  suffered  the  same  change  by  age  as  they  do 
now;  but  we  have  no  reason  to  suppose  they  possessed  any 
remedy  for  the  defect.    With  what  regret,  therefore,  must  the 
ancients  have  observed  the  first  appearance  of  this  change  in 
their  eyes,  which,  in  a  few  years,  must  render  them  compara- 
tively useless,  during  the  remainder  of  their  days,  for  many 
of  the  most  important  purposes  of  life ! 

461.  The  angle  of  vision  of  a  body  is  the  angle  made  by  two 
lines  drawn  from  its  opposite  sides  to  the  eye.    It  is  sometimes 

A  «,  called  the  visual  angle  of 

the  body.  Thus,  let  AB, 
figure  212,  be  an  object 
placed  before  an  eye,  E; 
the  angle  made  at  E  by  the 
two  lines  AE  and  BE  is 
the  visual  angle.  The  mag- 
nitude of  this  angle  for  any  object,  it  will  be  seen,  depends 
upon  its  distance  from  the  eye ;  for  if  the  object  is  removed 
farther  off,  as  to  A'  B',  the  two  lines  drawn  from  its  extremi- 
ties to  the  eye  approach  nearer  to  each  other,  or,  in  other 
words,  do  not  make  so  great  an  angle  with  each  other  as  when 
situated  at  A  B.  So  if  it  was  placed  nearer  to  the  eye  the  angle 
would  be  larger,  as  will  readily  be  seen. 

462.  It  is  upon  the  size  of  the  visual  angle  that  the  apparent 
magnitude  of  an  object  seen  by  the  eye  depends.     As  the  rays 
of  light  from  an  object  cross  each  other  before  reaching  the 
retina,  it  is  evident  that  the  size  of  the  image  must  always  be 
in  exact  proportion  to  the  magnitude  .of  this  angle ;  hence, 

cles  that  answer  well  for  a  person  at  one  age  afterwards  become  useless  ? 
What  is  the  explanation  ?  460.  How  long  have  spectacles  been  used  ?  Did 
the  ancients  possess  any  remedy  for  this  defect  of  vision  ?  461.  What  is  the 
angle  of  vision  of  a.body  ?  Upon  what  does  the  magnitude  of  this  angle  for 
any  body  depend  ?  462.  Upon  what  does  the  apparent  magnitude  of  a  body 

20* 


234  NATURAL     PHILOSOPHY. 

when  an  object  is  situated  at  a  distance,  it  must  always  appear 
smaller  than  when  placed  near  the  observer.  This  we  well 
know  to  be  the  case.  For  this  reason  parallel  lines  seem  to 
the  eye  to  approach  each  other  as  they  recede.  Every  one  has 
observed  this  when  looking  at  the  rails  upon  a  railroad,  or  at 
the  rows  of  trees  on  the  opposite  sides  of  a  straight  turnpike. 
At  a  distance  they  seem  much  nearer  together  than  in  our  im- 
mediate vicinity. 

As  we  judge  of  the  magnitude  of  a  distant  object  by  the  mag- 
nitude of  the  visual  angle,  which,  as  we  have  seen,  depends 
upon  the  distance  of  the  object,  it  is  plain  that,  before  deter- 
mining the  size  of  the  object,  we  must  form  some  opinion  of 
its  distance. 

Oftentimes  we  are  aided  in  making  our  estimate  of  the  mag- 
nitude of  distant  objects  by  other  objects  in  their  vicinity,  the 
size  of  which  is  known ;  but  if  a  body  is  entirely  alone,  and  we 
have  no  means  of  determining  its  distance,  we  can  form  no 
correct  estimate  of  its  magnitude.  A  person  lying  upon  his 
back  in  the  open  air  perceives  a  fly  passing  before  him,  only  a 
few  feet  from  his  eye,  but  for  a  moment  he  takes  it  to  be  a 
large  bird  high  in  the  air,  until  some  of  its  motions,  or  some 
other  circumstance,  reveals  its  true  character.  As  soon  as  this 
is  known  he  judges  correctly  of  the  distance,  but  before  any 
circumstance  occurred  to  indicate  the  real  character  of  the 
object,  or  its  distance,  he  was  utterly  unable,  by  the  mere 
formation  of  the  image  on  the  retina,  to  determine  either. 

463.  When  an  object  is  brought  nearer  to  the  eye  than  the 
least  distance  of  distinct  vision  (§  447),  it  becomes  confused, 
because  the  eye  is  then  unable  to  bring  the  rays  to  a  focus  on 
the  retina ;  on  the  other  hand,  if  it  is  carried  so  far  from  the 
eye  as  to  diminish  the  angle  of  vision  beyond  a  certain  limit, 
it  becomes  invisible,  the  image  being  too  small  to  produce  the 
sensation  of  sight. 

464.  The  eye  always  perceives  an  object  in  the  direction 
from  which  the  light  from  the  object  came  on  entering  it,  with- 
out reference  to  any  change  of  direction  it  may  previously  have 
undergone,  either  by  reflection  or  refraction;  hence  the  image 
of  an  object  seen  in  a  plain  mirror  appears  to  be  "behind  it. 
This  is  true,  not  only  of  an  object  considered  as  a  whole,  but 
also  of  all   its  parts.    Suppose  three  small  objects,  ABC, 

depend?  How  do  parallel  lines  that  recede  from  the  eye  appear?  What 
example,  that  is  frequently  seen,  is  mentioned?  Do  we,  in  judging  of  the 
magnitude  of  a  body,  first  judge  of  its  distance  ?  How  are  we  oftentimes 
aided  in  forming  our  estimate  of  a  distant  object  ?  Why  will  a  person  look- 
ing upward  in  the  open  air  often  mistake  a  fly  moving  near  him  for  a  large 
bird  at  a  distance  ?  463.  Why  is  an  object  not  seen  clearly  when  brought 
nearer  than  the  least  distance  of  distinct  vision  ?  May  an  object  be  removed 
so  far  from  the  eye  as  to  become  invisible  ?  464.  What  is  the  direction  in 
which  an  object  always  appears  to  the  eye  ?  Is  this  true,  also,  of  all  the 


VISION 


235 

figure  213,  placed 
one  above  another 
before  an  eye,  E, 
so  that  all  can  be 
seen  at  the  same 
time;  the  position 
of  each  is  clearly 
seen  by  the  direc- 
tion in  which  the 
Fis- m  light  comes  to  the 

eye.    A  is  seen  uppermost ;  then  B  a  little  below  it ;  then  C ; 

though  their  images  upon  the  retina,  a  b  c,  are  in  the  reverse 

order,  a  being  lowest,  then  b  above  it,  then  c. 

465.  Keeping  these  facts  in  view,  we  shall  have  no  difficulty, 
it  is  believed,  in  deciding  the  question  which  has  been  so  often 
discussed,  why  we  see  objects  erect  when  their  images  are 
found  inverted  on  the  retina  ?   For  suppose  the  objects,  instead 
of    being    sepa- 
rated, are  united 

in  one,  as  A  B, 
figure  214.  The 
part  A,  it  is  evi- 
dent, must  be 
seen  above  B, 
because  of  the  di- 
rection in  which  p.  214 
the  light  comes 

from  it,  as  really  as  if  it  were  a  separate  object ;  and,  for  the 
same  reason,  the  part  B  must  be  seen  beiow  A,  though  at  the 
same  time  the  image,  6,  of  the  part  B  is  above  a,  the  image  of 
the  part  A.  The  same  might,  of  course,  be  said  of  all  the  other 
points  in  the  object,  A  B. 

It  appears,  then,  that  if  the  eye  always  sees  objects,  and,  of 
course,  the  different  parts  of  objects,  in  the  direction  from 
which  the  light  was  coming  from  them  to  the  eye  at  the  time 
of  entering  it,  the  appearance  of  the  object  in  an  erect  position 
is  a  necessary  consequence  of  the  inverted  position  of  the  image 
upon  the  retina,  and  that,  if  the  image  upon  the  retina  was 
erect,  to  the  eye  the  object  must  necessarily  appear  inverted. 

466.  To  make  this  still  plainer,  let  the  line  midway  between 
AB  and  a 6,  figure  213,  be  the  axis  of  the  eye;  then  if  a  were 
not  below  the  axis,  the  object  A  would  not  be  above  it,  and  if 
b  were  not  above  it,  the  object  B  could  not  be  below  it ;  or, 
supposing  the  two  objects,  A  B,  united  together,  and  a  6,  the 
images  of  its  parts,  if  the  image  were  not  formed  in  an  inverted 
position  on  the  retina,  the  eye  could  not  see  the  object  erect. 
That  the  eye  should  see  objects  erect  when  the  image  is  formed 

parts  of  an  object  ?  As  a  necessary  consequence  of  this,  must  the  image  on 
the  retina  be  inverted,  in  order  that  the  object  may  appear  erect  to  the  eye  ? 


236  NATURAL     PHILOSOPHY. 

on  the  retina  inverted,  therefore,  so  far  from  being  wonderful 
or  mysterious,  is  only  a  necessary  result  from  the  well  deter- 
mined fact  that  every  object,  or  the  parts  of  an  object,  will 
always  appear  to  be  in  the  direction  from  which  the  light 
comes  to  the  eye.  If  the  light  from  an  object,  as  before  stated, 
or  any  part  of  an  object,  is  bent  out  of  its  course  during  its 
passage  to  the  eye,  then  the  object,  or  part  of  it,  from  which 
the  ray  was  emitted,  will  appear  to  be  situated  in  the  direction 
from  which  the  light  was  coming  as  it  entered  the  eye. 

467.  Another  circumstance  which 
has  occasioned  much  discussion  is 
the  well-known  fact  that,  though  in 
persons  whose  sight  is  perfect  there 
must  always  be  two  images  formed, 
one  on  the  retina  of  each  eye,  yet  only 
0  a  single  object  is  seen.  But  it  is  be- 
lieved this  results  entirely  from  the 
circumstance  that  when  a  person  looks 
at  an  object  he  directs  the  axes  of  both 
eyes  towards  it.  Thus,  when  a  person 
looks  at  a  near  object,  as  represented 
in  figure  215,  both  eyes  are  turned  in- 
wards, so  that  their  axes  produced 
would  meet  in  the  object,  O.  When 
- 215-  he  looks  at  a  more  distant  object  they 

will  be  less  turned  inwards,  as  in  figure  216;  and  when  the 
object  is  very  distant,  the  axes  of  the  eyes  will  be  nearly 
parallel.  As  each 
eye,  then,  sees  the 
object  in  the  direc- 
tion from  which  the 
light  comes  to  it,  it 
will  appear  to  both 
in  the  same  posi- 
tion, or,  which  is 
the  same  thing,  but 
one  object  will  be 
perceived.  If,  by 
any  means,  the  ax- 
es of  both  eyes  do 
not  point  precisely 

to    the     object,    it        

will  appear  double. 

This  may  be  easily  shown  by  looking  at  a  window,  and  press- 

Quest.  467.  Is  there  always  an  image  of  the  object  formed  in  each  eye  ? 
Why,  then,  does  not  the  object  appear  double?  How  are  the  axes  of  the 
eyes  directed  when  looking  at  an  object  ?  What  will  be  the  effect  if  the 
axes  of  both  eyes  are  not  directed  precisely  to  the  object?  How  may  this 
be  shown  ? 


VISION.  237 

ing  gently  with  the  finger  against  the  lower  side  of  one  of  the 
eyes,  by  which  its  axis  will  be  turned  a  little  upward ;  the  hori- 
zontal bars  will  then  all  appear  double:  but  if  he  presses 
against  the  right  or  left  side  of  one  of  his  eyes,  the  upright 
bars  will  be  doubled. 

468.  Persons  addicted  to  squinting,  in  which  one  or  both  of 
the  eyes  are  turned  out  of  their  natural  position,  always  see 
objects  double,  but  by  long  experience  they  acquire  the  habit 
of  attending  to  the  sensation  of  only  one  eye  at  a  time. 

469.  The  optic  nerve,  as  we  have  seen,  enters  the  eye  at  a 
point  about  y^th  of  an  inch  from  the  axis,  on  the  side  towards 
the  nose ;  at  this  point  there  is  a  space  of  some  extent,  some- 
times  called  the  punctum  ccecum,  that  is  quite  insensible  to  the 
action  of  light.     To  determine  this,  let  a  person  place  three 
small  wafers  about  three  inches  apart  on  a  sheet  of  white  paper 
before  him,  and  then,  shutting  the  left  eye,  let  him  hold  his 
head  within  six  or  eight  inches  of  the  paper,  ju'st  so  that  he 
can,  with  his  right  eye,  see  all  the  wafers.     Then,  keeping  his 
left  eye  closed,  let  him  look  attentively  at  the  wafer  at  the  left 
hand,  and  gradually  remove  his  head  from  the  paper  to  the 
distance  of  twelve  or  fourteen  inches,  and  the  middle  wafer 
will  entirely  disappear,  while  the  two  at  the  outside  are  clearly 
seen. 

470.  Impressions  made  on  the  retina  continue  for  a  certain 
time,  and  therefore  a  person  does  not  lose  sight  of  an  object  by 
winking.     If  a  red-hot  iron,  or  a  piece  of  burning  charcoal,  is 
made  to  revolve  ten  times  a  second,  the  eye  will  perceive  a 
continuous  circle  of  fire,  which  could  not  take  place  unless  the 
impression  on  the  retina  remained  a  tenth  of  a  second.     Some 
writers  affirm  that  it  remains  about  one-seventh  of  a  second. 

Taking  advantage  of  this  property  of  the  eye,  the  toy  called 
the  thaumatrope  has  been  constructed.  It  consists  of  a  circu- 
lar piece  cut  out  of  a  card,  with  two  threads  fixed  to  it  on  op- 
posite edges,  by  twisting  which  between  the  thumb  and  finger 
it  may  be  made  to  revolve  with  some  rapidity.  On  the  oppo- 
site side  of  the  card  two  objects,  having  some  relation  to  each 
other,  are  painted  in  the  proper  position,  so  that  when  the  card 
is  twirled  round  they  appear  connected,  both  objects,  though 
on  opposite  sides  of  the  card,  being  seen  at  the  same  time. 

Quest.  468.  Must  persons  addicted  to  squinting  always  see  objects  double  ? 
What  habit  is  acquired  by  them  which  to  some  extent  remedies  the  diffi- 
culty ?  469.  Where  does  the  optic  nerve  enter  the  eye  ?  What  is  meant 
by  the  punctum  caecum?  How  may  the  existence  of  such  an  insensible  point 
be  proved  ?  470.  Do  impressions  produced  on  the  retina  remain  for  a  time  ? 
If  a  piece  of  red-hot  iron  or  burning  charcoal  is  made  to  revolve  ten  times  a 
second,  what  will  be  the  appearance  to  the  eye  ?  What  length  of  time, 
then,  must  the  impression  remain  on  the  retina?  What  does  the  thauma- 
trope consist  of?  How  is  it  used  ?  Do  we  see  both  sides  of  the  card  at  the 
same  time  ? 


238  NATURAL     PHILOSOPHY. 

Let  A  B,  figure  217,  be  one  side 
of  a  circular  card,  with  a  cage 
painted  upon  it,  and  C  D  the 
}p  other  side,  with  the  figure  of  a 
bird  upon  it.  Now,  when  the 
card  is  twirled  round  as  sup- 
posed, the  bird  will  appear  as 
if  quietly  perched  in  the  cage, 
both  figures  being  seen  with 

equal  distinctness.  Sometimes  a  horse  is  painted  on  one  side 
of  the  card  and  the  rider  upon  the  other,  who,  by  the  motion 
of  the  card,  is  made  to  appear  seated  properly  upon  his  steed 
This  is  occasioned  by  the  permanence,  for  a  time,  of  the  sen- 
sation upon  the  retina;  an  image  of  the  object  upon  one  side 
of  the  card  is  first  formed,  and  remains  until  the  card  is  brought 
around  so  as  to  bring  the  figure  upon  the  other  side  in  view. 
The  consequence  is,  as  above  stated,  that  both  figures  are 
really  seen  at  the  same  time. 

The  intelligent  student,  who  is  unaccustomed  to  drawing, 
may  easily  prepare  an  apparatus  of  the  kind  by  procuring 
pieces  of  paper  with  the  necessary  pictures,  and  pasting  them 
on  the  opposite  sides  of  the  circular  piece  of  card. 

471.  Persons  are  occasionally  met  with  whose  eyes  appear 
to  be  insensible  to  particular  colours,  while  they  can  distin- 
guish all  others  with  certainty,  and  their  sight  is,  in  other  re- 
spects, perfect.     In  the  cases  which  occur  most  frequently  the 
individual  confounds  red  with  green,  not  only  mistaking  one 
for  the  other  when  presented  to  him  alone,  but  even  being  un- 
able to  distinguish  one  from  the  other  when  presented  to  him 
together,  considering  them  "  a  good  match." 

A  tailor  has  been  known  to  repair  an  article  of  dress,  the  colour  of 
which  was  black,  with  crimson,  not  noticing-  the  difference ;  and  an  officer 
in  the  navy  once  purchased  a  blue  uniform  coat  and  vest,  with  red  breeches 
to  match. 

472.  If  a  slip  of  white  paper  half  an  inch  wide  is  held  about  a  foot  from 
the  eye,  and  the  attention  directed  to  some  object  beyond  on  the  opposite 
side  of  the  room,  after  a  few  trials  it  will  appear  double.     If,  now,  a  can- 
die  is  brought  very  near  to  one  eye,  so  as  not  to  shine  upon  the  other,  the 
slip  of  paper  appearing-  on  the  side  next  to  the  light  will  seem  to  be  of  a 
yellowish  red,  while  that  on  the  other  side  will  be  of  a  pale  green.    If  the 
slip  of  paper  is  made  so  wide  that  one  image  overlaps  the  other,  one  side 
will  appear  red  and  the  other  green,  but  the  overlapping  part  will  be 
white. 

It  will  be  observed  that  the  two  colours  which  are  seen  are 
complementary  to  each  other,  but  no  full  explanation  of  the 
phenomenon  has  yet  been  given. 

Quest.  471.  What  is  said  of  the  eyes  of  certain  persons  in  respect  to  cer- 
tain colours  ?  In  the  cases  which  occur  most  frequently,  what  colours  are 
mistaken  for  each  other  ? 


VISION.  239 

473.  The  eyes  of  most  of  the  larger  land  animals  are  similar 
to  those  of  man,  but  they  are  often  more  or  less  modified,  tcr 
adapt  them  better  to  their  particular  modes  of  life.    Several  of 
these  peculiarities  in  the  eyes  of  animals  have  already  been 
alluded  to  (H51)- 

474.  The  eyes  of  insects  are  generally  compound ;  that  is, 
each  eye  is  composed  of  many  separate  eyes,  situated  side  by 
side.     This  is  the  case  with  the  eye  of  the  common  house-fly, 
the  beetle,  butterfly,  and  the  dragon-fly.     This  appears  to  be 
designed  to  compensate  for  the  want  of  motion  in  the  eye, 
which,  in  such  cases,  is  always  fixed.     They  are  thus  enabled 
to  see  in  different  directions  at  the  same  time. 

The  eye  of  the  butterfly,  when  examined  by  the  microscope, 
is  found  to  be  divided  into  an  immense  number  of  little  squares, 
by  a  firm  partition,  in  each  of  which  is  a  perfect  eye.  In  the 
yellow  beetle  these  little  cells  are  six-sided,  like  the  cells  of  a 
honey-comb,  but  much  smaller. 

The  eyes  of  insects  being  so  small,  they  can,  no  doubt,  per- 
ceive much  smaller  objects  than  man  is  capable  of  seeing,  but 
at  the  same  time  their  vision  cannot  extend  so  far. 

OPTICAL    INSTRUMENTS. 

Several  optical  instruments  have  already  been  in  part  de- 
scribed, as  the  different  kinds  of  mirrors  and  lenses ;  but  others 
of  great  importance,  mostly  formed  of  combinations  of  these, 
remain  to  be  noticed. 

475.  Photometers. — An  instrument  designed  to  determine  the 
relative  intensities  of  different  lights  is  called  a  photometer; 
several  of  which  have  been  invented,  but  no  one  of  them  has 
come  into  general  use.     There  seems,  indeed,  to  be  no  better 
method  to  determine  the  relative  intensities  of  two  or  more 
lights  than  that  proposed  by  Count  Rumford.     Let  us  suppose 
we  are  to  compare  the  intensities  of  the  light  from  two  lamps. 
They  are  to  be  taken  into  a  room  from  which  all  other  light  is 
excluded,  and  placed  in  front  of  a  white  screen ;  some  opake 
object  is  then  to  be  held  between  them  and  the  screen,  so  that 
the  shadows  formed  by  the  two  lamps  may  fall  side  by  side 
upon  the  screen.     If  the  two  shadows  are  not  now  of  equal 
intensity,  one  or  the  other  of  the  lamps  is  to  be  moved  back- 
ward or  forward  until  they  are  made  as  nearly  equal  as  pos- 
sible, and  then  the  distance  of  each  lamp  from  the  screen  is  to 
be  measured.     The  intensities  of  the  two  lights  will  be  to  each 
as  the  squares  of  these  distances.     Suppose,  for  instance,  that 

Quest.  473.  Are  the  eyes  of  most  land  animals  similar  to  those  of  man? 
474.  Of  what  are  the  eyes  of  most  insects  composed?  For  what  does  this 
appear  designed  to  compensate  ?  What  is  the  appearance  of  the  eye  of  the 
butterfly  when  examined  by  a  microscope  ?  475.  What  is  the  design  of  the 
photometer?  What  is  the  method  proposed  by  Count  Rumford  for  deter, 
mining  the  relative  intensities  of  two  or  more  lights? 


240  NATURAL     PHILOSOPHY. 

when  the  shadows  formed  by  the  two  lights  are  equal,  the  dis- 
tance of  the  first  from  the  screen  is  3  feet  and  that  of  the  second 
4  feet;  their  comparative  intensities  will  then  be  as  9  to  16. 

476.  The  Kaleidoscope.  —  The  kaleidoscope  is  an  instrument 
for  creating  and  exhibiting  beautiful  forms.     It  is  formed  by 
placing  two  pieces  of  painted  glass  together  in  such  a  manner 
that  the  angle  between  them  shall  be  an  exact  or  aliquot  part 
of  a  whole  circumference,  or  360  degrees,  and  enclosing  them 

in  a  case  so  as  to  exclude  all 
light  except  that  from  the  pro- 
per direction.  Let  A  and  B, 
figure  218,  be  two  plates  of 
glass  8  inches  long  and  2  inches 
wide,  painted  black  on  the  out- 
side, and  placed  as  in  the  figure, 
making  the  angle,  C,  between 
v.  O.Q  them,  60°,  or  just  one-sixth  of 

360°.  If  the  eye  be  now  placed 
at  E,  so  as  to  look  through  between  the  plates,  by  the  various 
reflections  of  the  plates  from  side  to  side,  the  angle  or  sector 
C,  will  appear  to  be  multiplied  five  times,  producing  the  circle 
of  six  sectors,  C,  C  1,  C2,  C  3,  C  4,  C  5.  If  any  small  object,  as 
a  piece  of  painted  glass,  is  placed  in  the  sector  C,  it  will,  of 
course,  appear  in  each  of  the  other  sectors,  C  1,  C2,  C  3,  &c., 
forming  a  symmetrical  figure  around  the  centre.  The  plates  are 
usually  enclosed  in  a  cylindrical  case,  and  several  pieces  of 
glass  of  different  colours  are  placed  in  C;  these,  by  turning  the 
instrument,  are  constantly  changing  their  position,  forming 
around  the  centre  of  the  circle  an  almost  endless  variety  of 
beautiful  figures. 

477.  The  Camera  Obscura.  —  The  camera  obscura  is  an  in- 
strument for  forming  images  of  objects,  as  of  a  landscape,  on 
a  screen  of  paper  or  other  substance  within  it.     The  name 
means  simply  darkened  chamber,  and  is  applied  to  the  instru- 
ment because  this  is  a  necessary  part  of  it ;  but,  as  we  shall 
hereafter  see,  it  may  be  a  large  room  to  contain  a  number  of 
persons,  or  very  small,  so  as  only  to  receive  the  screen  on 
which  the  image  is  formed,  the  observer  being  obliged  to  look 
in  through  a  small  aperture. 

478.  The  simplest  camera  obscura  that  can  be  formed  con- 
sists merely  of  a  small  aperture  in  the  window-shutter  of  a 
darkened  room,  before  which  a  screen  of  white  paper  is  to  be 
held.    Rays  of  light  received  through  a  small  aperture  upon  a 
screen  tend  to  form  an  image  of  the  object  from  which  they 
proceed,  and  not  an  image  of  the  form  of  aperture,  as  might 

Quest.  476.  What  is  the  kaleidoscope  ?  How  is  it  formed  *  477.  What  is 
the  camera  obscura?  What  is  the  meaning  of  the  name  ?  Why  is  it  used  ? 
478.  Of  what  does  the  simplest  camera  obscura  consist  ?  Will  rays  of  light 
passing  through  a  small  aperture  form  an  image  of  the  object  from  which 


VISION.  241 

be  supposed.  Thus,  if  the  light  of  the  sun  be  admitted  into  a 
room  otherwise  dark,  through  a  small  hole  in  the  shutter,  a 
round  image  of  the  sun  will  be  produced  upon  a  screen,  or  a 
sheet  of  paper,  held  at  a  little  distance  from  the  hole,  whatever 
may  be  its  form.  If  the  screen  is  held  too  near  the  hole,  how- 
ever, this  will  not  take  place,  but  a  luminous  spot  will  be  seen 
of  the  general  form  of  the  aperture,  with  its  angles  more  or 
less  rounded,  depending  upon  its  size  and  the  distance  the 
screen  is  held  from  it.  The  rounding  of  the  angles  is  evidently 
to  be  considered  as  an  approximation  to  the  form  of  the  sun. 
To  try  this  experiment,  let  a  large  hole  be  made  in  the  wooden 
shutter  of  a  room,  and  covered  with  a  sheet  of  lead,  in  which 
smaller  apertures  may  be  cut  at  pleasure,  of  any  form  desired. 
If  a  mere  slit  is  made  in  the  lead,  when  the  screen  is  held  near 
it  an  elongated  image  of  the  sun  will  be  formed ;  which,  how- 
ever, becomes  more  nearly  circular  as  the  screen  is  carried 
farther  off,  until,  at  length,  a  perfectly  circular  image  is  pro- 
duced. If  the  aperture  is  square  or  triangular,  or  whatever 
its  form,  the  same  result  will  be  obtained.  If  a  number  of 
small  pin-holes  are  made,  each  will  give  a  distinct  image  of  the 
sun  if  the  screen  is  held  near  them,  but  as  it  is  moved  farther 
off  they  will  increase  in  size  and  overlap  each  other  until  they 
combine  to  produce  a  single  large  and  well-defined  image,  just 
as  if  the  whole  space  of  the  shutter  in  which  they  are  contained 
had  been  removed,  except  that  it  is  less  brilliant.  If  a  circular 
aperture  is  made,  and  one  or  more  lines  drawn  across  it,  when 
the  screen  is  held  beyond  a  certain  distance  no  shadow  of  the 
lines  will  be  seen,  but  as  perfect  an  image  of  the  sun  as  if  they 
had  not  been  there, 

479.  To  understand  clearly  the  reason  of  this,  it  is  to  be  ob- 
served that  the  sun  presents  towards  us  a  disc  or  surface  of  a 
certain  extent,  from  each  point  of  which  rays  are  emitted,  so 
that  pencils  of  them  enter  even  small  apertures,  slightly  di- 
verging, and  crossing  each  other.  Now  a  larger  aperture,  as 
one  a  quarter  of  an  inch  square,  may  be  considered  as  made 
up  of  a  multitude  of  small  ones,  all  united  toge- 
ther ;  and  as  each  of  these  small  apertures  would 
produce  an  image  of  the  sun,  the  large  image 
may  be  supposed  to  be  composed  of  a  multitude 
of  small  images,  all  blended  together.  Thus,  if 
we  form  a  small  square,  A  B  C  D,  figure  219,  and 
from  points  in  its  sides  draw  several  small  cir- 
cles, it  will  be  seen  the  outline  of  the  whole  very 

they  proceed  ?  Will  this  be  the  case  whatever  may  be  the  form  of  the  aper- 
ture itself?  What  will  be  the  effect  if  the  screen  is  held  too  near  the  aper- 
ture ?  How  may  the  experiment  be  tried  ?  If  a  number  of  small  pin-holes 
be  made  in  the  shutter,  will  the  light  from  the  sun  still  form  an  image  of  the 
sun  upon  a  screen  within  ?  Must  the  screen  be  held  at  a  distance  from  the 
aperture  ?  477.  Do  the  rays  from  the  sun  cross  each  other  in  passing  through 

81 


242 


NATURAL     PHILOSOPHY. 


nearly  approximates  the  form  of  the  circle ;  and  the  deviation 
from  the  circular  form  becomes  less  and  less  in  proportion  as 
the  diameter  of  the  small  circles  is  increased.  Now,  as  has 
just  been  stated,  any  aperture,  whatever  may  be  its  form,  may 
of  course  be  considered  as  made  up  of  many  small  apertures; 
and  the  result  should  therefore  be  the  same,  viz :  the  produc- 
tion of  a  circular  image  of  the  sun. 

If  these  experiments  are  made  during  an  eclipse  of  the  sun, 
the  images  will  always  be  of  the  same  form  as  the  disc  of  the 
sun  towards  us.  It  is  said  that  during  an  eclipse  of  the  sun  an 
image  of  his  disc  has  been  seen  projected  on  the  ground  through 
the  small  opening  among  the  leaves  of  trees. 

480.  But  the  images  of  other  objects  may  be  formed  by  trans- 
mitting light  through  small  apertures  into  a  darkened  room,  as 

well  as  that  of  the  sun. 
Thus,  let  B,  figure  220, 
be  a  bird  standing  upon 
a  branch  of  a  tree  at  a 
little  distance  from  the 
window-shutter,  S,  of  a 
darkened  room;  if  the 
light  is  admitted  only 
through  a  small  hole  in 
the  shutter,  and  a  sheet 
of  paper  is  held  near  it,  a 
beautiful  inverted  image 
of  the  bird,  A,  will  be 
formed  upon  it.  If  the 
aperture  is  made  too  large  the  image  will  still  appear,  but  it 
will  be  confused  ;  and  if  too  small,  it  will  be  indistinct  for  want 
of  light. 

481.  But  a  much  better  image  will  be  formed  by  placing  in 
the  aperture  a  small  double  convex  lens;  the  aperture  may 
thus  be  made  much  larger,  and  therefore  a  greater  quantity 
of  light  will  be  admitted,  by  which  the  brilliancy  of  the  image 
will  be  greatly  increased.     If  the  sheet  of  paper  is  oiled  before 
using  it,  so  as  to  make  it  translucent  (§  334),  the  image  will  be 
seen  with  nearly  equal  distinctness  on  both  sides  at  the  same 
time,  and  the  experiment  may  be  conveniently  shown  to  a 
large  audience  in  the  room.     Sometimes  the  lens  is  fitted  into 
a  hollow  ball,  which  is  so  adjusted  in  the  shutter  as  to  allow 
of  being  turned  in  different  directions,  and  thus  different  por- 
tions of  the  landscape  in  front  may  be  successively  exhibited. 

an  aperture  ?  May  a  large  aperture  be  considered  as  made  up  of  many  small 
ones  ?  What  will  be  the  result  if  the  experiment  is  made  during  an  eclipse 
of  the  sun  ?  480.  May  the  images  of  other  objects  be  formed  in  the  same 
manner  as  those  of  the  sun  ?  What  will  be  the  effect  if  the  aperture  is  made 
too  large  ?  481.  What  will  be  the  effect  if  a  double  convex  lens  is  placed  in 
the  aperture  ?  Why  will  the  image  be  more  brilliant  ?  What  is  the  appa< 


Fig.  220. 


VISION 


243 


Persons  standing  in  front  of  it  will  have  their  images  painted 
so  distinctly  on  the  screen  within  the  room  that  they  can  be 
easily  recognized  Such  a  piece  of  apparatus  is  called  a  sci- 
optic  ball. 

482.  The  common  portable  camera  obscura  is  constructed 
essentially  on  the  same  principle  as  the  above,  but  is  adapted 
for  tracing  upon  paper  the  outlines  of  landscapes  and  other 
objects,  in  front  of  which  it  may  be  placed.  It  is  usually  made 
of  a  square  box,  A  B  C  D,  figure  221,  in 
the  top  of  which  is  fitted  a  tube  contain- 
ing a  lens  and  a  plane  mirror,  M,  in- 
clined so  as  to  reflect  the  light  from  an 
adjacent  landscape  directly  through  the 
lens  to  the  bottom  of  the  box,  as  in- 
dicated by  the  dotted  lines.  Having 
placed  the  instrument  upon  a  table  be- 
fore the  landscape  or  building,  the  form 
of  which  is  to  be  traced,  and  adjusted 
the  parts  in  a  proper  manner,  a  well- 
defined  image  is  formed  upon  the  paper 
on  the  bottom  of  the  box.  In  the  side 
A  C  is  a  large  opening,  through  which 
the  person  has  access  to  his  paper,  and 
all  extraneous  light  is  excluded  by 


Fig.  221. 


means  of  a  black  curtain,  L,  which  is  drawn  over  him.  The 
person  stands,  as  will  be  seen,  with  his  back  towards  the  ob- 
ject, and  traces  it  accurately  at  his  leisure,  by  means  of  the 
image  on  the  paper  before  him.  To  diminish  spherical  aberra- 
tion (§  376),  instead  of  a  double  convex  lens,  a  meniscus  is  often 
used,  as  represented  in  the  figure.  The  tube  containing  the 
lens  is  made  moveable,  in  order  to  adjust  the  lens  to  the  proper 
distance  from  the  paper,  which  will  depend  upon  the  distance 
of  the  object  from  the  mirror. 

An  improved  form  of  this  instrument  has  been  constructed 
within  a  few  years  past,  in  which  the  lens  and 
mirror  are  combined  in  a  single  piece.     This 
consists  of  a  triangular  prism,  ABC,  figure  222, 
with  one  of  its  sides,  A  B,  convex,  and  another, 
B  C,  concave ;  so  that  the  rays  of  light,  on  enter- 
ing the  convex  side,  which  is  placed  towards  the 
object,  are  made  to  converge,  and  are  totally  re-  B 
fleeted  downward  by  the  internal  surface,  AC.         i?ig.  222. 

ratus  called  when  the  lens  is  fitted  in  a  hollow  ball  and  placed  in  the  shutter, 
so  as  to  be  capable  of  being  turned  in  different  directions  ?  482  For  what 
is  the  common  portable  camera  obscura  adapted  ?  Where  is  the  paper  to 
l>e  laid  on  which  the  image  of  the  object  is  to  be  traced  ?  For  what  purpose 
is  there  a  large  opening  in  one  side  of  the  box  ?  How  is  the  light  excluded? 
Why  is  a  meniscus  used  instead  of  a  double  convex  lens  ?  What  kind  of  a 
glass  is  used  in  the  improved  apparatus  illustrated  in  figure  222  ? 


244 


NATURAL     PHILOSOPHY. 


Fig.  223. 


As  the  side  B  C  is  made  concave,  the  effect  is  the  same  as  that 
of  the  meniscus,  to  diminish  the  aberration.  It  is  plain  that 
the  concavity  of  the  side  BC  should  be  less  than  the  convexity 
of  A  B,  in  order  that  the  rays  may  be  made  to  converge  to  a 
focus  on  the  paper. 

483.  The  camera  lucida  is  an  instrument  used  for  the  same 
purpose  as  the  camera  obscura  ;  that  is,  for  making  drawings 
of  landscapes,  buildings,  and  other  objects.     It  is  made  with  a 

single  glass  of  the  form  A  B  C  D, 
figure  223,  having  all  its  sur- 
faces carefully  polished.  If  an 
object,  as  M  N,  is  placed  before 
it,  so  that  the  rays  may  enter 
the  lower  part  of  the  side  A  D 
perpendicularly,  they  will  be 
'totally  reflected  from  the  in- 
ternal surface,  D  C,  to  C  B,  and 
from  that  to  the  eye  at  E,  caus- 
ing the  object  to  appear  as  if  situated  at  m  n.  If,  now,  the  eye 
is  placed  near  the  angle  B,  so  that  one  half  of  the  pupil  may 
receive  the  light  directly  from  the  paper  on  the  table  at  mn, 
the  outline  of  the  object  may  be  traced  upon  it  with  a  pencil. 
The  effect  of  the  instrument,  therefore,  is  to  bring  the  reflected 
image  of  the  object  upon  the  paper  on  which  it  is  to  be  traced. 
The  glass  is  usually  enclosed  in  a  socket  of  brass,  except  those 
parts  through  which  the  light  is  to  pass,  and  supported  by  a  rod, 
with  a  clamp  and  screw,  to  attach  it  firmly  to  the  side  of  a  table. 

484.  The  Magic  Lantern.  —  This  is,  to  a  considerable  extent, 
the  reverse  of  the  camera  obscura.     By  the  camera  obscura  a 
diminished  image  of  a  landscape  or  other  object  is  formed  on  a 

screen  within,  but  by  means  of 
the  magic  lantern  a  magnified 
image  of  a  small  object  is  formed 
on  a  screen  without.  The  ob- 
jects used  are  generally  small 
and  nearly  transparent  paint- 
ings, made  on  glass  ;  an  entirely 
opake  object  cannot  be  used. 
This  instrument,  as  usually 
made,  consists  of  a  tin  box, 
painted  black  inside  and  out, 
with  a  lamp,  L,  figure  224,  and  a  reflector,  M  N,  by  which  a 
strong  light  is  thrown  upon  the  object,  so  as  to  produce  a 
brilliant  image.  On  the  side  of  the  lamp  opposite  the  reflector 
is  a  tube,  A  B,  having  a  large  plano-convex-lens,  A,  and  a 

Quest.  483.  For  what  purpose  is  the  camera  lucida  used  ?  What  is  the 
effect  of  this  instrument  ?  484.  How  does  the  magic  lantern  differ  from  the 
camera  obscura?  What  are  the  objects  generally  used  in  this  piece  of  ap- 
paratus ?  Of*what  does  this  instrument  consist  ?  What  is  the  design  of  the 


VISION.  245 

smaller  double  convex  lens,  B.  Through  C  D  is  a  slit  for  in- 
troducing the  paintings,  of  which  there  are  generally  several 
on  the  same  piece  of  glass;  so  that  one  after  another  may  be 
exhibited  by  sliding  through  the  piece  of  glass.  The  design  of 
the  lens  A  is  to  concentrate  the  strongest  light  possible  upon 
the  object,  which  is  to  be  situated  a  little  beyond  the  focus  of 
the  double  convex  lens,  B.  The  rays  of  light  from  the  object 
or  picture  are  then  refracted  by  the  second  lens,  B,  and  brought 
to  a  focus  upon  a  screen,  GF,  placed  at  the  proper  distance, 
producing  on  it  an  inverted  image.  The  lens  B  is  usually  con- 
tained in  a  smaller  tube,  which  slides  in  the  other,  so  that  it 
may  be  drawn  out  or  pushed  in  at  pleasure,  to  accommodate 
the  instrument  to  the  distance  of  the  screen.  The  farther  off 
this  is  placed,  the  more  will  the  object  be  magnified,  but  the 
light  being  spread  over  so  great  a  surface,  if  the  image  is  too 
much  magnified,  it  becomes  indistinct.  This  instrument  is  al- 
ways used  in  the  evening,  or  in  a  dark  room.  The  drawing 
supposed  to  be  in  the  lantern  in  figure  224  is  a  representa- 
tion of  an  eclipse  of  the  sun— S,  the  sun ;  M,  the  moon ;  E,  the 
earth. 

485.  The  solar  microscope  is  constructed  on  the  same  prin- 
ciple as  the  magic  lantern,  except  that  it  is  adapted  for  using 
the  light  of  the  sun  instead  of  that  of  a  lamp.    The  light  is  first 
reflected  into  the  instrument,  which  is  placed  in  a  hole  in  the 
window-shutter,  by  means  of  a  mirror  so  contrived  as  to  be 
moved  steadily  in  the  proper  position  for  reflecting  the  light 
of  the  sun,  in  the  required  direction,  at  any  hour  near  the  mid- 
dle of  the  day.     The  lenses  are  exactly  the  same  as  those  of 
the  magic  lantern,  except  that  the  one  corresponding  to  B, 
figure  224,  by  which  the  image  is  formed,  is  usually  much 
smaller,  and  magnifies  more. 

The  solar  microscope  is  generally  used  for  forming  images 
of  objects  in  natural  history,  as  small  insects,  parts  of  plants, 
&c.  No  light,  of  course,  must  be  admitted  into  the  room,  ex- 
cept that  which  forms  the  image. 

486.  The  Single  Microscope.  —  The  single   microscope,   or 
magnifying-glass,  is   simply  a  double  convex   lens,  through 
which  the  observer  looks  at  the  object.    When  used,  no  image 
is  formed,  but  the  eye  looks  directly  at  the  object  itself.    It  is 
often  fitted  up  in  a  case  of  horn  or  shell,  so  as  to  adapt  it  to  be 
carried  in  the  pocket. 

large  lens,  A  ?  Why  is  the  second  lens,  B,  usually  contained  in  a  smaller 
tube,  which  slides  in  the  larger  ?  How  will  the  magnitude  of  the  image  be 
affected  by  increasing  the  distance  of  the  screen  ?  Will  the  light  be  as  bril- 
liant ?  485.  How  is  the  solar  microscope  constructed  ?  In  what  does  it  differ 
from  the  magic  lantern  ?  For  what  purpose  is  the  solar  microscope  gene- 
rally used  ?  486.  What  is  the  single  microscope,  or  magnifying -glass  f 
How  does  the  eye  look  at  the  object  when  it  is  used  ? 

21* 


246  NATURAL     PHILOSOPHY. 

487.  The  reason  why  the  double  convex  lens  magnifies  the 
apparent  size  of  objects  may  be  illustrated  as  follows: — Let  L, 

figure  225,  be  a  double 
convex  lens,  and  A  B  an 
object  seen  through  it  by 
the  eye,  E.  Let  the  dark 
lines  drawn  from  the  ex- 
tremities, A  and  B.  to  the 
lens  be  the  outermost 

rays  that  reach  the  eye ;  in  passing  thrqugh  the  lens  they  are 
bent  inwards  towards  the  axis,  and  the  eye  sees  the  points 
from  which  they  were  emitted  in  the  direction  from  which  they 
were  coming  when  entering  it.  That  is,  the  eye  will  see  the 
extremities,  A  and  B,  of  the  object  as  if  situated  at  A'  and  B' ; 
and,  as  the  points  between  A  and  B  will  be  affected  in  the 
same  manner,  it  is  evident  that  the  object,  AB,  will  appear  to 
be  enlarged  to  A'  B'. 

488.  By  means  of  the  double  convex  lens  we  are  able  to  see 
objects  much  nearer  the  eye  than  we  otherwise  could:  indeed, 
it  is  only  when  seen  at  a  less  distance  than  in  ordinary  vision 
that  any  magnifying  effect  is  produced.   The  magnifying  power 
of  such  a  lens  is  determined  by  dividing  the  least  distance  of 
distinct  vision  (5  inches)  by  the  distance  at  which  it  is  seen 
by  the  use  of  the  glass ;  or,  which  comes  to  the  same  thing,  by 
the  focal  distance  of  the  glass.     Thus,  suppose  a  magnifying- 
glass  enables  the  eye  to  see  clearly  an  object  at  the  distance 
of  2|  inches,  it  will  appear  twice  as  large  as  when  viewed  by 
the  naked  eye.     If  the  object,  by  the  use  of  the  glass,  can  be 
seen  when  held  only  one  inch  from  the  eye,  it  will  be  magnified 
five  times;  that  is,  it  will  appear  five  times  as  large  as  when 
viewed  by  the  unassisted  eye. 

489.  If  a  small  object  is  viewed  through  a  perforation  in  a 
piece  of  paper,  or  other  thin  opake  substance,  it  will  appear 
magnified.     This  is  because  the  more  diverging  rays  from  the 
object,  which  would  otherwise  enter  the  eye,  are  excluded  by 
the  paper,  and  the  object  is  seen  by  the  less  divergent  rays ;  so 
that  it  can,  in  consequence,  be  brought  nearer  the  eye.     Let 
O,  figure  226,  be  a  small  object  seen  by  the  eye,  E,  through  a 
perforation  in  a  piece  of  black  paper,  P;  the  perforation  irTthe 
paper  being  smaller  than  the  pupil  of  the  eye,  the  outside  and 

Quest.  487.  What  is  illustrated  in  figure  225  ?  How  does  it  appear  that 
the  object  will  be  seen  magnified  ?  488.  Are  we  able,  by  means  of  the 
magnifying-glass,  to  see  objects  when  held  nearer  the  eye  than  we  other- 
wise could  ?  How  is  the  magnifying  power  determined?  If,  by  means  of 
a  double  convex  lens,  the  eye  is  enabled  to  see  an  object  at  the  distance  of 
Scinches,  what  will  be  its 'magnifying  power  ?  If  the  object  is  seen  dis- 
tinctly at  the  distance  of  an  inch  only,  how  much  will  it  be  magnified  ? 
489.  Will  a  small  object  appear  magnified  if  seen  through  a  small  aperture 
made  in  some  opake  substance  ?  How  is  it  explained  ? 


247 


Fig.  226. 

most  divergent  rays  of  the  pencil  that  would  otherwise  enter 
the  eye  are  now  intercepted,  and  the  object  is  seen  by  the 
smaller  pencil,  represented  by  the  continuous  lines;  and  it 
may,  therefore,  be  brought  nearer  the  eye.  If  the  outside  rays, 
represented  by  the  dotted  lines,  were  permitted  to  enter  the 
eye,  they  would  not  be  brought  accurately  to  a  focus  on  the 
retina,  but  would  tend  to  form  an  image  a  little  beyond  it,  by 
which  the  vision  would  be  obscured.  It  is  this  circumstance 
that  prevents  most  persons  from  seeing  objects  clearly  when 
brought  nearer  than  about  5  inches. 

490.  It  should  be  noted  here,  that  always  when  speaking  of 
the  magnifying  power  of  any  instrument,  the  linear  magnify- 
ing power  is  meant,  unless  it  is  otherwise  stated.    Thus,  when 
it  is  said  that  the  magnifying  power  of  a  glass  is  2  or  5,  as 
above,  it  is  meant  that  the  apparent  length  of  a  straight  line 
will  be  increased  in  that  proportion.     At  the  same  time,  the 
surface  will  be  magnified  in  a  much  greater  ratio,  as  the  expert 
arithmetician  will  instantly  see.     Thus,  when  the  linear  mag- 
nifying power  of  an  instrument  is  2,  the  surface  will  be  mag- 
nified twice  2,  or  4  times ;  and  when  the  linear  magnifying 
power  is  5,  the  surface  will  be  magnified  5  times  5,  or  25  times. 
The  superficial  magnifying  power  is  always  found  by  squaring 
the  linear  magnifying  power. 

These  remarks  are  intended  to  apply  to  all  instruments,  both 
microscopes  and  telescopes. 

491.  If  a  piece  of  glass  or  other  transparent  substance, 

ground  and  polished,  with 
several  plane  faces,  is  held 
between  the  eye  and  some 
small  object,  there  will  be 
seen  as  many  objects  as 
there  are  faces  to  the  glass. 
This  is  called  a  multiplying 
glass.  Let  MN,  figure  227, 
be  a  glass  of  this  kind,  hav- 
Fig<  227.  ing  a  plane  surface  towards 

Quest.  490.  What  is  meant  by  the  linear  magnifying  power  of  an  instru- 
ment ?  When  the  linear  magnifying  power  of  an  instrument  is  2,  how  much 
will  the  surface  be  magnified  ?  491.  What  is  the  multiplying  glass  ? 


248  NATURAL     PHILOSOPHY. 

the  eye,  E,  and  three  plane  faces  on  the  side  towards  the 
object,  A.  To  the  eye,  E,  there  will  appear  to  be  three  ob- 
jects, which  will  be  seen  with  nearly  equal  clearness.  A  por- 
tion of  the  rays  from  the  object,  A,  passing  perpendicularly 
through  the  glass  at  the  middle  face,  will  not  be  bent  out  of 
their  course,  but  other  portions,  coming  in  contact  with  the 
other  two  faces,  will  be  bent  inward  to  the  eye,  so  that  the 
object  will  be  seen,  in  accordance  with  laws  already  pointed 
out  (§  444),  in  the  directions  B  and  C.  Glasses  of  this  kind  are 
sometimes  made  with  a  great  number  of  faces,  through  each 
of  which  the  object,  if  small,  will  be  seen. 

492.  The  Compound  Microscope.  —  The  compound  micro- 
scope  receives  its  name  from  the  fact  that  it  is  composed  of  two 
or  more  lenses,  whereas,  in  the  single  microscope,  there  is  but 
one.  Let  A  B,  figure  228,  be  a  compound  microscope,  having 


Pig.  228. 

its  object-glass,  A,  which  is  towards  the  object,  and  eye-glass, 
B,  which  is  towards  the  eye ;  and  let  O  be  a  small  object  be- 
fore it.  By  means  of  the  small  object-glass  an  image  of  the 
object  will  be  formed  within  the  tube,  as  at  I,  which  will  be  as 
much  larger  than  the  object  as  it  is  farther  from  the  lens  (§  375). 
Thus,  suppose  the  object,  O,  is  only  a  quarter  of  an  inch  from 
the  centre  of  the  object-glass,  A,  while  the  image,  I,  is  formed 
at  the  distance  of  2  inches,  it  will  then  be  8  times  as  large  as 
the  object.  Now,  by  means  of  the  eye-glass,  B,  we  view  the 
image  precisely  as  we  do  the  object  with  the  single  micro- 
scope ;  and  if,  by  means  of  this,  we  are  able  to  see  the  image 
at  the  distance  of  one  inch,  .while  the  least  distance  of  distinc- 
vision  to  the  unaided  eye  is  5  inches,  the  whole  magnifying 
power  of  the  instrument  will  be  5  times  8,  or  40.  If  the  dis- 
tance of  the  object  from  the  object-glass  was  only  jVth  of  an 
inch,  and  the  image  formed  at  the  distance  of  6  inches,  it  would 
be  magnified  6  times  10,  or  60  times;  and  if  the  same  eye-glass 
were  used  as  before,  the  whole  magnifying  power  of  the  in- 
strument would  be  5  times  60,  or  300.  If  an  eye-glass  of  only 
half  this  focal  distance,  or  ^Vth  of  an  inch,  were  used,  its  mag- 
nifying power  would  be  600. 

Quest.  492.  How  many  lenses  are  there  in  the  compound  microscope  ? 
What  is  the  object-glass?  What  is  the  eye-glass?  What  is  the  office 
performed  by  each  ?  Will  the  image  formed  by  the  object-glass  be  larger 
or  smaller  than  the  object  ?  If  the  distance  of  an  object  from  the  object- 
glass  be  one-tenth  of  an  inch,  and  the  image  be  formed  at  the  distance  of  6 
inches,  how  much  will  it  be  magnified?  If,  now,  an  eye-glass  is  used, 
which  enables  the  eye  to  look  at  the  image  at  the  distance  of  one  inch,  how 
great  will  be  the  whole  magnifying  power  of  the  instrument  ? 


VISION. 


249 


493.  The  field  of  view  of  an  instrument,  as  a  microscope,  or 
telescope,  is  the  field  or  space  the  eye  is  capable  of  taking  in 
at  a  single  view  when  using  it.  This,  in  a  microscope  with 
only  two  glasses,  as  described  above,  is  exceedingly  small ; 
and  to  increase  it,  a  third  lens  has  been  added,  called  a  field- 
glass. 

To  make  this  plain,  let  us  suppose  an  attempt  is  made  to 
construct  the  instrument  without  the  field-glass.  Let  A,  figure 
229,  be  the  object-glass,  and  B  the  eye-glass;  O  is  a  small 


Fig.  229. 

object  placed  before  it,  of  which  a  magnified  image,  mn,  is 
formed.  This  image,  it  will  be  seen,  exceeds  the  diameter  of 
the  object-glass,  B,  and  the  rays  from  a  part  of  it  only,  which 
lies  between  p  and  g,  can  reach  the  eye  at  E.  Though  the 
object  may  not  exceed  ^th  or  ^th  of  an  inch  in  lengtlCthere- 
fore,  only  a  part  of  it  will  be  seen  by  the  eye. 
But  let  us  now  introduce  the  field-glass,  as  F,  figure  230 ; 

the  rays   which  would, 
if  this   were  not   used, 
form  the  image  mn,  as 
before,  are  now  brought 
•  sooner  to  a  focus,  and 
produce  the  image  ppt 
the  whole  of  which  will 
be  seen  through  the  eye- 
Fjg-230'  glass,  B.    The  image  be- 

ing diminished,  the  object  will,  as  a  matter  of  course,  appear 
less  magnified  than  it  would  otherwise  be;  but  the  field  of  view 
is  so  much  enlarged  that,  on  the  whole,  the  instrument  is  found 
to  be  much  improved. 

The  glasses  of  the  compound  microscope  are  usually  care- 
fully adjusted  at  the  proper  distances  in  a  tube  of  brass,  with 
an  apparatus  for  holding  the  objects  to  be  examined,  and  a 
concave  mirror  or  convex  lens  for  illuminating  them  strongly ; 
and  the  whole  attached  to  a  proper  support. 
A  camera  lucida  is  also  often  added  to  the  larger  instrument, 

Quest.  493.  What  is  meant  by  the  field  of  view  of  an  instrument  ?  What 
is  the  object  of  the  field-glass  ?  Will  the  object  appear  as  much  magnified 
by  the  use  of  the  field-glass  as  it  otherwise  would  be  ? 


250  NATURAL     PHILOSOPHY. 

for  the  purpose  of  making  drawings  of  objects  as  they  appear 
when  viewed  by  them. 

494.  Telescopes. — Telescopes  are  the  reverse  of  the  com- 
pound microscope ;  their  design  is  to  enable  us  to  view  objects 
which  are  so  distant  as  not  to  be  seen  at  all  by  the  unassisted 
eye,  or  but  indistinctly. 

Telescopes  are  of  two  kinds,  the  reflecting  and  the  refracting, 
both  of  which  are  much  in  use,  each  possessing  its  peculiar 
advantages. 

495.  It  seems  to  be  tolerably  well  ascertained  that  telescopes 
of  some  kind  were  known  about  six  hundred  years  ago,  but 
they  were  probably  very  imperfect,  and  no  very  accurate  de- 
scription of  them  has  come  down  to  us.     The  Galilean  tele- 
scope, from  the  name  of  its  inventor,  Galileo,  who  first  made  it 
public  in  the  year  1609,  is  the  oldest,  the  construction  of  which 
is  now  known. 

This  instrument  is  made  with  a  double  convex  object-glass, 
A  B,  and  a  double  concave  eye-glass,  C  D,  as  shown  in  figure 
231.  Let  MN  be  an  object  situated  at  a  distance  before  it,  so 


Fig.  231. 

that  an  inverted  image  will  be  formed  by  the  object-glass,  AB, 
at  ran,  if  the  concave  eye-glass,  C  D,  is  removed.  By  placing 
a  screen  at  this  point  the  image  received  upon  it  might  be  exa- 
mined directly,  but  the  eye,  placed  at  E,  could  not  perceive  the 
object,  since  the  rays  would  enter  it  converging,  which  is  in- 
consistent with  distinct  vision.  But  if  a  concave  lens,  CD,  is 
introduced,  the  virtual  focus  (\  372)  of  which  shall  be  at  the 
point  where  the  image  would  fall,  the  rays  will  emerge  parallel, 
and  produce  a  distinct  image  in  the  eye. 

This  telescope,  in  consequence  of  the  small  field  of  view  it 
affords,  is  not  used  now,  except  for  viewing  objects  at  a  mode- 
rate distance,  as  in  a  large  room  or  theatre.  It  is  then  called 
an  opera-glass.  Usually  two  of  them  are  attached  to  each 
other,  at  such  a  distance  that  one  eye  may  be  directed  through 
each  at  the  same  time. 

496.  If,  instead  of  the  concave  lens  for  an  eye-glass,  the  con- 
vex lens  is  introduced,  the  instrument  becomes  a  common 

Quest.  494.  What  is  the  design  of  the  telescope  ?  How  many  kinds  of  tele- 
scopes are  there  ?  In  what  do  they  differ  from  each  other  ?  495.  How  long 
have  telescopes  been  in  use  ?  What  is  the  old  jst  telescope,  the  construction 
of  which  is  now  known?  If  the  eye-glass  were  removed,  why  could  not  an 
eye  placed  at  E,  fig.  231,  see  the  object?  What  purpose  is  served  by  the 
eye-glass  ?  For  what  purposes  only  is  this  instrument  now  used  ?  494. 
YVhat  change  only  is  required  in  this  telescope  to  convert  it  into  an  astrono- 


VISION.  251 

astronomical  telescope;  but  the  eye-glass  must  then  be  placed 
farther  from  the  object-glass,  as  will  shortly  be  shown,  and  the 
object  will  be  seen  inverted.  The  astronomical  telescope  is 
represented  in  figure  232,  in  which  A  B  is  the  object-glass  and 


CD  the  eye-glass.  The  object-glass  is  formed  with  a  long 
focal  distance,  but  the  eye-glass  with  a  focal  distance  much 
less ;  upon  this  depends  its  magnifying  power.  Let  M  N  be  an 
object  placed  at  a  distance  from  the  object-glass,  so  as  to  form  an 
inverted  image,  mn,  at  its  principal  focus,  in  the  manner  already 
described  (§  375);  this  image  will  then  be  viewed  by  means  of 
the  eye-glass,  C  D,  just  as  in  the  compound  microscope. 

Indeed,  there  is  a  striking  resemblance  between  the  astrono- 
mical telescope  and  the  compound  microscope.  In  the  latter 
instrument  a  magnified  image  of  the  object  is  formed,  which  is 
viewed  by  means  of  the  eye-glass,  as  a  single  microscope;  but 
in  the  telescope  a  diminished  image  is  formed,  which  is  viewed 
in  the  same  manner  as  before.  But  though  the  image  of  the 
object  in  the  telescope  is  very  much  less  than  the  object  itself, 
yet  its  apparent  magnitude  is  often  greatly  increased,  since  we 
are  enabled  to  inspect  the  image  at  a  much  less  distance  from 
the  eye  than  the  object  is. 

497.  In  order  to  determine  the  magnifying  power  of  the  tele- 
scope, let  us  first  suppose  the  image,  mn,  received  upon  a 
screen ;  this  image  will  be  as  much  less  than  the  object  as  it  is 
nearer  the  lens,  A  B,  than  the  object  is  (§  375),  but  if  the  eye 
were  situated  in  the  lens,  A  B,  the  apparent  magnitude  of  both 
would  be  the  same.  This  appears  from  the  fact  that  at  this 
point  both  would  subtend  the  same  angle,  as  will  readily  be 
seen  by  examination.  Let  us  suppose,  now,  that  the  focal  dis- 
tance of  the  object-glass,  that  is,  the  distance  from  AB  to  mn, 
is  10  inches,  and  that  the  eye  is  so  placed  as  to  view  the  image 
at  the  least  distance  of  distinct  vision,  which  is  5  inches;  its 

mical  telescope  ?  Upon  what  does  the  magnifying  power  of  this  telescope 
depend  ?  What  purpose  is  served  by  the  object-glass,  and  what  purpose  by 
the  eye-glass  of  this  telescope  ?  What  is  said  of  the  resemblance  between 
this  telescope  and  the  compound  microscope  ?  If  the  image  of  an  object  in 
a  telescope  is  smaller  than  the  object  itself,  how  does  it  appear  that  its  ap- 
parent magnitude  may  be  increased  by  it  ?  497.  If  we  suppose  the  eye 
placed  in  the  object-glass  of  the  telescope,  and  the  image  received  upon  a 
screen,  what  win  be  the  comparative  apparent  magnitude  of  the  object  and 
image  as  seen  by  it  ?  How  does  this  appear  ?  If  the  focal  distance  of  the 
object-glass  be  10  inches,  and  the  image  be  viewed  directly  by  the  eye  at 


252  NATURAL    PHILOSOPHY. 

apparent  magnitude  would  evidently  be  twice  as  great  as  that 
of  the  object.  If  the  focal  distance  of  the  object-glass  were  5 
feet,  or  60  inches,  then,  to  the  naked  eye  placed  at  the  distance 
of  5  inches,  the  image  would  have  twelve  times  the  apparent 
magnitude  of  the  object  itself.  But  then  the  image  is  always 
viewed  by  means  of  an  eye-glass,  which  acts  precisely  as  a 
single  microscope,  and  enables  the  observer  to  see  it  when 
situated  much  nearer  the  eye  than  the  distance  mentioned,  5 
inches.  Let  us  suppose,  then,  that  by  means  of  the  eye-glass 
the  eye  is  enabled  to  see  the  image  at  the  distance  of  only  one 
inch,  by  which  it  would,  of  course,  be  magnified  5  times ;  the 
whole  magnifying  power,  in  the  last  case  mentioned  above, 
would  be  5  times  12,  or  60  times.  But  this  same  result  might 
evidently  have  been  obtained  by  dividing  the  focal  distance  of 
the  object-glass,  60  inches,  by  the  focal  distance  of  the  eye- 
glass, 1  inch  ;  hence,  to  find  the  magnifying  power  of  the  astro- 
nomical telescope,  we  have  only  to  divide  the  focal  distance  of 
the  object-glass  by  the  focal  distance  of  the  eye-glass. 

As  the  eye-glass  should  be  placed  so  as  to  have  the  image  in 
its  focus,  it  is  evident  the  distance  of  the  two  glasses  apart 
ought  to  be  just  equal  to  the  sum  of  their  focal  distances.  Ge- 
nerally the  object-glass  is  considerably  the  largest,  and  the  eye- 
glass is  placed  in  a  tube  somewhat  smaller  than  that  which 
contains  the  former,  so  that  it  may  be  moved  backward  and 
forward  as  may  be  found  necessary  in  viewing  objects  at  dif- 
ferent distances,  or  to  accommodate  the  instrument  to  the  eyes 
of  different  persons.  In  this  telescope  it  is  evident  that  ob- 
jects will  always  be  seen  inverted;  but  for  astronomical  pur- 
poses this  is  of  no  consequence,  since  their  true  place  and  po- 
sition can  be  just  as  readily  determined. 

498.  By  adding  to  the  astronomical  telescope  two  other 
lenses  of  the  same  focal  distance  as  the  eye-glass,  the  terres- 
trial telescope,  or  common  spy-glass  is  produced.  The  design 
of  these  additional  lenses  is  merely  to  cause  the  object  to  be 
seen  erect:  an  inverted  image  of  the  object  is  first  formed,  as 
in  the  instrument  just  described,  and  then  an  inverted  image 
of  this  image,  which  is  seen  by  the  eye  as  before. 

the  distance  of  5  inches,  how  would  the  apparent  magnitude  of  the  object 
and  image  compare  ?  How  does  the  eye-glass  act  ?  Does  it  enable  the 
observer  to  see  the  image  at  a  less  distance  from  the  eye  than  5  inches  ?  If 
the  focal  distance  of  the  object-glass  be  60  inches,  and  by  means  of  the  eye- 
glass the  image  may  be  viewed  at  the  distance  of  1  inch  only,  what  would 
be  the  magnifying  power  of  the  instrument  ?  How  is  the  magnifying  power 
of  the  telescope  to  be  found  ?  What  distance  apart  must  the  two  glasses  be 
placed  ?  Which  of  the  two  glasses  is  usually  largest  ?  Why  is  the  eye- 
glass placed  in  a  tube  so  as  to  allow  of  being  moved  backward  and  forward  ? 
How  will  the  object  always  be  seen  in  this  telescope  ?  498.  How  does  the 
terrestrial  telescope,  or  spy-glass,  differ  from  the  astronomical  telescope  just 
described  ?  What  is  the  design  of  these  two  additional  glasses  ?  What  is 


VISION.  253 

Figure  233  represents  the  glasses  of  the  terrestrial  telescope 
removed  from  the  tube.    AB  is  the  object-glass,  by  means  of 


Fig.  233. 

which  an  image,  mn,  of  the  object,  MN,  is  formed  in  its  focus; 
CD  corresponds  to  the  eye-glass  of  the  astronomical  telescope, 
and  is  so  placed  that  the  image,  m  n,  is  in  its  focus.  From  C  D 
the  rays  emerge  parallel,  and  by  the  second  eye-glass,  IF, 
are  again  brought  to  a  focus,  forming  an  image,  m1 '  n1 ',  of  the 
first  image,  which  is  erect  like  the  object.  This  last  image  is 
seen  by  the  eye  at  E,  magnified  by  the  third  eye-glass,  G  H. 
The  magnifying  power  of  this  telescope  is  found  in  the  same 
manner  as  in  the  astronomical  telescope,  by  dividing  the  focal 
distance  of  the  object-glass,  A  B,  by  that  of  the  first'eye-glass, 
C  D ;  the  effect  of  the  other  glasses,  as  already  intimated,  being 
only  to  reverse  the  position  of  the  first  image. 

These  three  eye-glasses  are  usually  fixed  in  a  tube,  in  the 
proper  position  with  respect  to  each  other,  so  as  to  slide  back- 
ward and  forward  in  the  tube  which  contains  the  object-glass, 
A  B.  As  a  portion  of  light  is  lost  at  every  refraction,  objects 
are  seen  less  distinctly  with  this  instrument  than  with  the 
astronomical  telescope ;  but,  as  it  shows  the  objects  erect,»it  is 
preferred  for  use  in  viewing  terrestrial  objects. 

Both  astronomical  and  terrestrial  telescopes  are  subject  to 
all  the  difficulties  attending  upon  spherical  (§  376)  aberration 
and  the  dispersion  of  the  colours  by  refraction,  but  our  limits 
will  not  allow  us  to  enter  upon  a  detailed  examination  of  the 
different  methods  adopted  for  obviating  them.  A  few  remarks 
only  upon  achromatic  telescopes  can  be  introduced.  They  are 
so  called  because  the  object  is  seen  in  them  destitute  of  every 
other  but  its  natural  colours. 

499.  Since  the  primary  colours  of  light  are  always  separated 
more  or  less  when  it  is  refracted,  this  effect  must  follow  when 
refraction  is  produced  by  means  of  a  lens,  as  well  as  when  the 
prism  is  used ;  but  the  colours,  instead  of  being  situated  as  in 
the  solar  spectrum  (\  387),  will  be  arranged  in  concentric  rings. 

represented  in  figure  233  ?  To  what  does  the  lens  C  D  correspond  in  the 
astronomical  telescope  ?  How  is  the  magnifying  power  of  the  terrestrial 
telescope  found?  Are  objects  seen  as  distinctly  by  means  of  the  terrestrial 
as  by  the  astronomical  telescope  ?  What  reason  is  given  ?  Are  telescopes 
subject  to  (he  difficulties  arising  from  spherical  aberration  and  the  dispersion 
of  the  primary  colours  of  light  ?  What  is  an  achromatic  telescope  ?  499. 
When  the  primary  colours  of  light  are  separated  by  the  action  of  a  lens,  how 
will  they  be  arranged  ?  To  destroy  the  colours  produced  by  a  double  convex 
22 


254  NATURAL     PHILOSOPHY. 

We  have  seen  that  when  two  similar  prisms  are  used,  having 
different  dispersive  powers,  and  placed  in  opposite  positions, 
the  light  will  still  be  bent  out  of  its  course,  but  the  colours 
will  nearly  disappear.  To  destroy  the  colours,  therefore, 
produced  by  the  double  convex  lens,  it  is  only  necessary  to 
connect  with  it  a  double  concave  lens,  made  of  glass  whose 
dispersive  power  is  greater  than  that  of  the  glass  of  which  the 
convex  lens  is  made.  The  concavity  of  the  concave  lens  being 
somewhat  less  than  the  convexity  of  the  other,  the  rays  will 
still  be  brought  to  a  focus,  though  at  a  greater  dis- 
tance  from  the  glass  than  if  the  concave  lens  were  not 
used,  forming  a  colourless  or  acromatic  image,  that  is, 
an  image  of  the  natural  colour  of  the  object. 

It  is  found  that  flint  glass  (that  of  which  drinking- 
glasses  are  usually  made)  and  crown  glass  (common 
window-glass)  answer  well  this  purpose,  the  disper- 
sive  power  of  the  former  being  considerably  greater 

F\«  234  ^an  tna*.  °^  ^e  ^a^ter-  Figure  234  represents  an 
achromatic  object-glass,  AB  being  a  convex  lens  of 
crown  glass,  and  C  D  a  concave  lens  of  flint  glass. 

500.  The  reflecting  telescope,  instead  of  the  object-glass,  con- 
tains a  concave  reflector,  or  speculum,  in  the  focus  of  which 
the  image  is  formed,  and  is  viewed  by  means  of  an  eye-glass, 
in  the  same  manner  as  in  the  refracting  telescope. 

There  are  several  kinds  of  reflecting  telescopes,  as  the  Gre- 
gorian, Newtonian,  Herschelian,  and  the  Cassegrainian,  each 
of  which  has  received  its  name  from  its  inventor. 

Figure  235  represents  the  Gregorian  telescope,  in  which  A  B 
is  a  concave  metallic  speculum,  with  a  hole  in  its  centre  and 


Fig.  235. 


C  D  a  much  smaller  one,  supported  so  as  exactly  to  front  the 
first.  By  means  of  a  screw,  W,  the  small  speculum  is  moved 
backward  and  forward,  so  as  to  adjust  it  at  the  proper  distance 
from  AB,  which  should  be  a  little  greater  than  the  sum  of  their 

lens,  what  only  is  necessary  ?  Must  the  concave  or  convex  lens  have  the 
greater  dispersive  power  ?  Must  the  concavity  of  the  concave  lens  equal  the 
convexity  of  the  convex  ?  What  two  kinds  of  glass  are  found  to  answer  the 
purposes  required  ?  500.  How  does  the  reflecting  telescope  differ  from  the 
refracting  ?  What  different  kinds  of  reflecting  telescopes  are  mentioned  ? 
How  many  reflectors  has  the  Gregorian  telescope  ?  Where  is  the  image 


VISION.  255 

focal  distances.  E  and  F  are  eye-pieces,  which  are  usually 
plano-convex  lenses,  having  their  convex  surfaces  turned  to- 
wards the  object.  Now  suppose  rays  of  light,  M  N,  from  the 
extremities  of  some  distant  object,  to  strike  upon  the  large  spe- 
culum, they  will,  of  course  (§  355),  be  reflected  to  a  focus,  and 
will  form  an  inverted  and  diminished  image,  mn,  in  front  of 
the  small  mirror,  a  little  farther  from  it  than  its  principal  focus. 
By  means  of  the  small  mirror,  light  from  this  image,  as  from  a 
new  object,  will  be  again  reflected  through  the  hole  in  the  large 
mirror,  and  a  second  erect  image  formed,  m!  n',  which  is  viewed 
magnified  by  the  eye-glass,  F.  The  lens  E  might  be  dispensed 
with,  but  is  always  used  for  the  same  purpose  as  the  field- 
glass  (§  493)  in  the  compound  microscope. 

The  Cassegrainian  telescope  is  precisely  the  same  as  the 
Gregorian,  except  that  the  small  mirror,  CD,  is  made  con- 
vex, so  that  the  length  of  the  instrument  is  somewhat  dimi- 
nished, the  virtual  image  of  the  small  mirror  being  formed 
behind  it. 

The  Newtonian  ielescope  was  invented  by  Sir  Isaac  Newton, 
and  is  shown  in  figure  236.  It  consists  of  a  concave  speculum, 


Fig.  236. 

A  B,  placed  at  one  end  of  a  tube,  from  which  rays  of  light,  MN, 
from  an  object  are  reflected  so  as  to  form  an  inverted  image, 
ran,  in  its  focus;  but  a  small  plane  mirror,  CD,  inclined  to  the 
axis  of  the  instrument,  is  interposed,  and  it  is  reflected  to  m'n', 
where  it  is  viewed  by  means  of  the  eye-pieoe. 

501.  It  only  remains  for  us  to  describe  the  telescope  of  Her- 
schel,  which,  for  astronomical  purposes,  seems  at  present  nearly 
to  have  superseded  all  others.  Superior  instruments  of  this 
kind  have  recently  been  made  in  this  country  by  Mr.  Amasa 
Holcomb,  of  South  wick,  Massachusetts. 

This  telescope  is  made  like  that  of  Newton,  except  that  the 
reflection  from  the  plane  mirror  is  avoided  by  inclining  the 
speculum,  A  B,  figure  237,  a  little  to  one  side,  so  that  the  image 
is  formed  on  that  side  of  the  tube,  as  at  E,  where,  of  course, 
the  eye-piece  is  placed.  The  head  of  the  observer  being  at  E, 

from  the  large  speculum  formed  ?  What  is  the  use  of  the  small  mirror  ? 
What  is  the  design  of  the  eye-glass  ?  By  whom  was  the  Newtonian  tele- 
scope invented?  Of  what  does  it  consist?  501.  In  what  does  Herschel's 
telescope  differ  from  the  Newtonian  ?  How  does  the  observer  stand  when 


256  NATURAL     P  II  I  L  O  S  O  P  II  Y. 

11* 

.-.^—  — M 


some  portion  of  the  rays,  M  N,  are  intercepted,  but  not  as  large 
a  portion  as  is  lost  by  the  reflection  from  the  plane  mirror  in 
Newton's  telescope.  In  viewing  near  objects,  too,  especially 
if  the  instrument  is  very  short,  some  distortion  of  the  image 
would  be  produced  ;  but  nothing  of  this  is  observed  when  it  is 
of  considerable  length  "and  used  for  astronomical  purposes,  for 
which  it  is  chiefly,  if  not  wholly,  intended.  In  using  this  in- 
strument the  observer,  of  course,  stands  with  his  back  towards 
the  object. 

The  magnificent  telescope  constructed  by  the  elder  Dr.  Her- 
schel  has  often  been  described.  The  speculum  it  contained 
was  4  feet  in  diameter,  and  had  a  focal  length  of  40  feet.  The 
highest  magnifying  power  of  the  instrument  was  6450,  which, 
however,  was  seldom  used,  a  lower  power  being  generally 
preferred. 

Recently  a  still  larger  telescope  has  been  constructed  in  Ire- 
land, by  the  Earl  of  Rosse.  The  form  of  this  telescope  is  the 
same  as  that  of  Herschel's,  just  described ;  but  the  great  spe- 
culum is  much  larger,  being  6  feet  in  diameter,  and  having  a 
focal  distance  of  54  feet.  Its  thickness  is  5£  inches,  and  its 
weight  nearly  4  tons. 

Little  use  has  yet  been  made  of  this  leviathan  instrument,  as 
it  is  not  yet  entirely  finished,  but  the  few  observations  made 
with  it  are  said  to  have  been  very  satisfactory. 


CHAPTER    VII. 

MAGNETISM. 

502.  MAGNETISM  is  the  science  which  treats  of  the  properties 
and  effects  of  the  magnet.  This  is  an  ore  of  iron,  pieces  of 
which  have  been  long  known  to  possess  the  power  of  attract- 
ing each  other,  as  well  as  pieces  of  iron  and  steel,  when  brought 

using  this  telescope  ?  What  was  the  diameter  of  the  speculum  in  Herschel's 
great  telescope  ?  What  was  its  focal  distance  ?  What  is  the  diameter  and 
focal  distance  of  the  leviathan  telescope  recently  constructed  by  the  Earl  of 
Rosse  ?  502.  What  is  magnetism  ?  What  is  the  magnet  ?  What  peculiar 
property  does  it  possess  ? 


MAGNETISM.  257 

in  their  vicinity.  The  name  magnet,  given  to  pieces  of  this  ore, 
is  said  to  be  derived  from  Magnesia,  a  town  in  Greece,  from 
which  they  were  obtained. 

503.  This  ore  of  iron  is  now  found  in  almost  every  country, 
and  is  usually  called  loadstone.    Sometimes  pieces  of  it  are  cut 
into  regular  forms,  and  used  as   magnets.     They  are  often 
called  natural  magnets,  to  distinguish  them  from   artificial 
magnets,  to  be  hereafter  described. 

If  a  mass  of  this  ore  of  iron,  of  tolerably  regular  form,  be 
rolled  in  iron  filings,  there  will  generally  be  found  two  points, 
and  only  two,  nearly  opposite  each  other,  on  which  the  filings 
chiefly  collect;  between  these  points  few  only  will  adhere. 
These  points  where  the  filings  collect  are  called  the  poles  of 
the  magnet.  N  S,  figure  238,  repre- 
sents a  natural  magnet  which  has 
thus  been  rolled  in  iron  filings ;  N 
and  S  are  the  poles  around  which 
the  filings  chiefly  collect.  If  the 
magnet  be  placed  upon  a  piece  of 
wood  in  a  basin  of  water,  the  piece 
of  wood— supposing  it,  of  course,  capable  of  floating  in  the 
water  with  the  loadstone  upon  it — will  turn  round,  whatever 
may  be  its  position  at  first,  so  that  one  of  the  two  poles  shall 
be  towards  the  north,  which  is  therefore  called  the  north  pole, 
and  the  other  towards  the  south,  and  is  therefore  called  its 
south  pole.  Its  tendency  thus  to  arrange  itself  is  called  its  di- 
rective property,  and  has  been  long  known.  Often  pieces  of 
loadstone  are  seen  of  so  regular  a  form  that  they  may  be  sus- 
pended by  a  cord,  so  as  readily  to  place  themselves  in  this 
position. 

504.  When  two  magnets  made  to  float  upon  water,  as  de- 
scribed above,  are  brought  near  each  other,  it  will  be  found 
that,  when  two  north  poles  or  two  south  poles  are  presented 
together,  they  repel  each  other,  but  when  a  north  and  a  south 
pole  are  presented  together,  they  attract  each  other.   We  have, 
therefore,  this  principle,  that  like  poles  repel,  but  unlike  poles 
attract  each  other. 

505.  The  natural  magnet  has  the  power  of  communicating 
its  properties  to  pieces  of  steel  simply  by  being  brought,  for  a 
short  time,  in  contact  with  them.  ^  They  are  then  said  to  be 
magnetized,  and  are  called  artificial  magnets.    In  examining 

Quest.  503.  Is  this  ore  of  iron  very  commonly  found  ?  What  is  it  called  ? 
If  a  piece  of  the  native  magnet  is  rolled  in  iron  filings,  what  is  the  result  ? 
If  the  magnet  is  placed  upon  a  piece  of  wood  capable  of  floating  with  it 
in  a  basin  of  water,  in  what  direction  does  it  settle  ?  What  is  the  north 
and  what  the  south  pole  of  the  magnet  ?  What  is  meant  by  the  directive 
property  of  the  magnet  ?  504.  When  two  magnets,  floating  upon  separate 
pieces  of  wood  in  a  basin  of  water,  are  brought  near  each  other,  what  is  ob- 
served? 505.  Does  the  natural  magnet  have  the  power  of  communicating 
its  properties  to  pieces  of  steel  ?  What  are  artificial  magnets  ?  May  either 


258  NATURAL    PHILOSOPHY. 

the  phenomena  of  magnetism  it  is  of  no  importance  whether 
we  use  the  natural  or  artificial  magnet;  but  as  the  latter  can 
more  easily  be  made  of  any  form  desired,  and  is  much  less 
liable  to  be  accidentally  broken,  it  is  usually  preferred.  The 
north  pole  of  an  artificial  magnet  usually  has  a  line  drawn 
across  it,  to  distinguish  it. 

A  small  bar  of  steel,  magnetized  in  the  manner  described, 

and  suspended  at  its  centre 
of  gravity  upon  a  pivot,  so  as 
to  move  freely,  constitutes  the 
magnetic  needle.  Figure  239  re- 
presents an  instrument  of  this 
kind.  When  the  needle  is  sus- 
pended in  this  manner,  what- 
ever may  be  its  position  at  first 
as  to  the  meridian,  when  left  to 
itself,  after  a  few  oscillations  it 
soon  settles  in  the  direction  of 
north  and  south,  the  north  pole, 
N,  being  to  the  north,  and  the 
south  pole,  S,  to  the  south. 

506.  Two  needles  of  this  kind  serve  well  to  perform  the  ex- 
periment described  above  (\  504)  as  being  made  with  two  natu- 
ral magnets  placed  upon  pieces  of  wood  floating  in  water. 
When  two  similar  poles  are  brought  near  together,  a  strong 
repulsion  is  observed;  but  if  the  poles  are  unlike,  there  will  be 
an  equally  strong  attraction.     The  repulsion  or  attraction  is 
mutual,  no  doubt,  and  both  the  needles  move  more  or  less  if 
they  are  free ;  but  if  one  is  held  in  the  hand,  while  one  of  its 
poles  is  presented  to  the  other  needle,  that  alone,  of  course, 
can  move,  though  the  force  exerted  between  them  is  mutual. 

507.  When  pieces  of  iron  are  attracted 
by  a  magnet,  they  always  become  them- 
selves magnetic.     Let  N  S,  figure  240,  be 
a  magnetic  bar,  and  let  a  piece  of  soft 
iron,  B,  be  presented  to  its  south  pole,  S, 
it  will  be  instantly  attracted  ;  and  if  it  is 
examined  while  held  in  contact  with  the 
magnetic  bar,  it  will  be  found  that  its 
lower  end  is  a  south  pole  and  its  upper 

end  a  north  pole.    If  a  second  piece,  C,  be  Pig.  340. 

natural  or  artificial  magnets  be  used  in  investigating  the  phenomena  of  mag- 
netism ?  How  is  the  north  pole  of  an  artificial  magnet  usually  marked]? 
What  is  the  magnetic  needle?  When  the  needle,  properly  suspended,  is 
left  to  itself,  in  what  direction  does  it  settle  ?  If  the  two  similar  poles  of  two 
needles  are  brought  near  each  other,  what  is  the  effect  ?  If  the  poles  are 
dissimilar,  what  is  the  effect  ?  Is  the  repulsion  or  attraction  between  the 
needles  mutual?  507.  What  effect  is  produced  on  a  piece  of  iron  when  it 
is  attracted  by  a  magnet  ?  Does  the  extremity  of  a  piece  of  iron,  in  contact 
with  one  of  the  poles  of  a  magnet,  possess  the  same  or  the  opposite  polarity  ? 


MAGNETISM.  259 

now  presented  to  the  first,  it  will  be  likewise  attracted,  and 
will  become  magnetic,  its  upper  end  being  a  north  pole  and 
its  lower  end  a  south  pole,  as  before.  Other  pieces  still  might 
be  attached  in  like  manner,  and  each  would  become  mag- 
netic, but  the  magnetism  of  each  successive  piece  will  be 
weaker  and  weaker. 

It  will  be  particularly  observed  that  the  upper  end  of  the  iron 
bar,  which  becomes  a  north  pole,  is  in  contact  with  the  south 
pole  of  the  magnet.  This  is  always  the  case ;  the  south  pole 
of  a  magnet  always  induces  a  north  pole  in  that  part  of  a  piece 
of  iron  which  is  next  to  it,  while  the  part  farthest  from  it  will 
be  a  south  pole.  So,  when  a  piece  of  iron  is  presented  to  the 
north  pole  of  a  magnet,  the  part  next  to  the  magnet  becomes 
a  south  pole,  while  the  other  part  becomes  a  north  pole. 

508.  But,  though  the  pieces  of  iron  are  so  readily  magnet- 
ized, they  do  not  retain  their  magnetism.  This  may  be  shown 
by  taking  hold  of  the  piece  B  and  removing  it  from  the  mag- 
net; its  magnetism  is  instantly  destroyed,  as  will  be  shown  by 
the  dropping  of  the  other  pieces  attached  to  it. 

The  development  of  magnetic  properties  in  a  piece  of  iron 
in  this  manner,  merely  by  the  approach  of  one  of  the  poles  of 
a  magnet,  is  called  magnetic  induction,  from  its  analogy  to 
electrical  induction,  to  be  hereafter  explained.  Though  we 
have  supposed  the  iron,  in  the  above  experiment,  in  contact 
with  the  magnet,  this  is  not  necessary ;  it  only  requires  to  be 
brought  near  to  it.  This  may  be  shown  by  holding  the  piece 
of  iron  at  a  little  distance  from  the  pole  of  the  magnet,  and  then 
presenting  to  one  end  of  the  iron  another  small  piece,  which  it 
will  be  found  to  attract,  though  it  will  cease  to  hold  it  if  re- 
moved too  far  from  the  magnet.  But  when  the  piece  of  iron 
is  in  contact  with  the  magnet,  its  magnetism  is  stronger. 

The  same  thing  may  be  familiarly  illustrated  as  follows : — 
Lay  a  large  nail  upon  a  piece  of  window-glass,  and  place  near 
one  end  of  it  some  small  tacks,  or  other  pieces  of  iron ;  no  ap- 
pearance of  attraction  between  them  and  the  nail  will  be  at 
first  observed.  Holding  the  glass  in  one  hand,  with  the  nail 
upon  it  and  small  tacks  scattered  upon  one  end,  bring  one  pole 
of  the  magnet  under  the  glass,  near  the  other  end  of  the  nail ; 
the  tacks  will  be  seen  to  be  instantly  attracted  by  the  nail,  by 
reason  of  the  magnetism  induced  in  it  by  the  influence  of  the 
magnetic  pole  beneath  the  glass.  But  the  nail,  it  will  be  ob- 
served, has  not  been  in  contact  with  the  magnet,  for  the  glass 
has  all  the  time  been  between  them. 

When  a  piece  of  iron  becomes  magnetic  by  being  in  contact  with  a  magnet, 
will  it  attract  a  second  piece  ?  508.  What  is  the  effect  of  carefully  removing 
the  magnet  from  the  first  piece  ?  What  is  meant  by  magnetic  induction  ? 
That  magnetism  may  be  induced  in  a  piece  of  iron,  must  it  be  in  contact 
with  the  magnet  ?  Is  the  induced  magnetism  strongest  when  the  iron  is  in 
contact  with  the  magnet  ?  May  magnetism  be  induced  in  iron  through  a 


260 


NATURAL     PHILOSOPHY. 


This  leads  us  to  remark,  further,  that  the  inductive  influence 
is  exerted  through  all  other  substances  that  are  not  themselves 
capable  of  becoming  magnetic,  and  without  any  diminution  of 
the  effect.  Thus  the  magnetism  induced  in  a  bar  of  iron,  held 
at  a  given  distance  from  one  of  the  poles  of  a  magnet,  will  be 
of  the  same  intensity,  whether  a  plate  of  glass  or  copper,  or  a 
piece  of  wood,  be  held  between  them,  or  whether  a  stratum  of 
air  only  intervenes. 

509.  The  attraction  of  a  piece  of  iron  by  a  magnet  seems  to 
be  in  consequence  simply  of  the  magnetism  first  induced  in  it; 
and  the  reason  why  other  substances  are  not  also  attracted  is 
because  they  are  not  capable  of  becoming  magnetic. 

510.  When  a  magnet  acts  upon  a  bar  of 
iron  to  induce  magnetism  in  it,  its  own  mag- 
netism is  always,  at  the  same  time,  increased 
by  the  reaction  of  the  magnetism  of  the  bar 
upon  the  magnet.     This  may  be  shown  by 
direct  experiment.     Let  A,  figure  241,  be  a 
bar  magnet,  suspended  to  a  common  lamp- 
stand,  S;  B  a  small  piece  of  soft  iron,  with 
a  scale-pan  and  weights,  W,  attached   by 
means  of  cords.     With  this  it  will  be  easy 
to  determine  the  weight  the  magnet  is  capa- 
ble of  sustaining;  and  when  this  is  done,  let 
a  bar  of  soft  iron,  about  equal  in  size  to  the 
magnet,  be  held  againstthe  upper  end  of  the 
magnet.   If  trial  is  now  made,  it  will  be  found 
that  more  weight  will  be  sustained  by  the 
magnet  than   before  the  iron  was  placed 
above  it. 

511.  If  the  north  poles  or  south  poles  of 
two  magnets  are  both  together  brought  in 
contact  with  one  end  of  a  bar  of  iron,  the 

magnetism  induced  in  it  will  be  more  intense  than  if  one  alone 
had  been  used  ;  but  the  effect  will  be  still  greater  if  the  bar  of 
iron  is  placed  between  the  two  magnets,  so  that  the  north  pole 
of  one  magnet  shall  be  in  contact  with  one  extremity,  and  the 
south  pole  of  the  other  magnet  in  contact  with  the  other  extre- 
mity. .Both  magnets  then  conspire  to  produce  the  same  result, 
and  the  effect  is  the  greatest  possible. 

When  the  north  pole  of  a  magnet  is  placed  against  the  centre 
of  a  bar  of  iron,  a  complex  effect  is  produced;  the  centre  of  it 

piece  of  glass?  Is  the  inductive  influence  exerted  through  other  sub- 
stances ?  509.  Why  may  not  other  bodies  besides  iron  and  steel  be  attracted 
by  the  magnet  ?  510.  When  a  magnet  acts  upon  a  piece  of  iron  to  induce 
magnetism  in  it,  how  is  its  own  magnetism  affected  ?  How  may  this  be 
shown  ?  511.  How  must  two  magnets  be  presented  to  a  bar  of  iron,  in  order 
to  produce  the  greatest  inductive  influence  ?  What  is  the  effect  when  the 
north  pole  of  a  magnet' is  brought  in  contact  with  the  centre  of  an  iron  bar  ? 


MAG  N  ETISM. 


261 


Fig.  242. 


243- 


becomes  a  south  pole,  while  the  two  extremities  of  it  are  both 
north  poles,  figure  242.  If  the  south  pole  had 
been  used,  the  middle  of  the  bar  would,  of  course, 
have  been  a  north  pole,  and  the  two  ends  south 
poles.  If  the  north  pole  of  a  magnet  is  placed 
on  the  centre  of  a  star  made  of  sheet  iron,  so  as 
to  be  perpendicular  to  it,  as  is 
shown  in  figure  243,  the  centre 
becomes  a  south  pole,  and  all  the 
extremities  of  the  rays  north  poles 
of  weak  intensity.  tt> 

512.  A  curious  and  not  uninstructive  experi- 
ment may  be  performed  with  two  straight  mag- 
nets and  a  piece  of  soft  iron,  made  in  the  form  of  " 
the  letter  Y.  Let  a  b  C,  figure  244, 
be  this  piece  of  iron,  which  may  be 
suspended  by  one  of  the  branches 
to  the  north  pole  of  one  of  the  magnets,  as  A.  Its 
lower  end  will  immediately  become  a  north  pole, 
and  will  be  capable  of  sustaining  a  small  piece  of 
iron,  as  a  key  ;  but  if,  while  held  in  this  manner, 
the  south  pole  of  the  other  magnet,  B,  be  brought 
in  contact  with  the  other  branch,  b,  of  the  piece 
of  iron,  the  key  will  instantly  drop  off.  This  is 
occasioned  by  the  opposing  action  of  the  two 
magnets,  neutralizing  each  other's  influence. 
The  branch  a  will  have  a  south  polarity,  and  the 
branch  b  a  north  polarity,  while  the  lower  extre- 
mity will  be  neutral. 

513.  We  have  seen  that  though  pieces  of  iron 
so  readily  become  magnetic,  under  the  influence 
of  a  magnet  placed  in  their  vicinity,  they  do  not  retain  their 
magnetism  after  being  removed  from  the  magnet.  It  is  other- 
wise with  pieces  of  steel  properly  tempered  ;  they  do  not  be- 
come magnetic  as  readily  as  pieces  of  iron,  but  when  the  mag- 
netic property  is  once  induced  in  them,  they  retain  it  perma- 
nently. When  one  end  of  a  piece  of  steel  of  considerable 
length  is  brought  near  one  of  the  poles  of  a  magnet,  it  does 
not  instantly  become  magnetic  through  its  whole  extent,  as  a 
bar  of  iron  does,  but  it  requires  a  perceptible  time  for  the  mag- 
netic influence  to  reach  the  further  end.  Sometimes  the  steel 
bar  is  divided  into  several  parts,  there  being  several  north  and 
south  poles  in  succes- 
sion. Let  A,  figure  245, 

bar  of  steel,placed  very  Pig.  345. 

Quest.  512.  What  curious  experiment  is  illustrated  in  figure  244  ?  513. 
Do  pieces  of  steel  retain  their  magnetism  when  they  have  been  once  mag- 
netized ?  Is  the  magnetic  virtue  as  readily  induced  in  steel  as  in  iron  ? 


Fig.  244. 


262  NATURAL     PHILOSOPHY. 

near  its  north  pole,  but  not  actually  in  contact  with  it.  If  the 
bar  be  now  examined  by  means  of  a  very  short  and  delicate 
magnetic  needle,  it  will  be  found  to  have  a  south  pole  at  the 
end  nearest  the  magnet,  and  a  north  pole  at  the  other  end; 
but  between  these  will  be  other  weak  north  and  south  poles, 
alternating  with  each  other,  as  indicated  by  the  letters  s  and  n. 
These  points,  where  the  polarities  thus  change  from  one  to  the 
other,  are  called  consecutive  points,  and  their  occurrence  very 
much  weakens  the  general  magnetic  power  of  the  bar. 

514.  It  is  a  remarkable  fact  that  if  a  magnet  be  broken  into 
two  or  more  parts,  all  the  pieces  will  instantly  be  found  to  be 
perfect  magnets;  that  is,  each  of  them  will  have  both  a  north 
and  a  south  pole,  though  the  point  at  which  they  were  separated 
was  before  perfectly  neutral.     This  experiment  may  easily  be 
performed  by  magnetizing  a  piece  of  a  watch-spring,  and  then 
breaking  it  in  the  centre  and  examining  closely  the  two  pieces. 

515.  When  a  magnet  is  used  for  inducing  magnetism  in 
pieces  of  iron  or  steel,  it  loses  nothing  of  its  own  power;  but, 
on  the  contrary,  its  own  magnetism  is  rather  increased  ($  509), 
if  it  was  not  before  at  a  maximum.     It  seems,  therefore,  that 
nothing  has  been  given  up  by  it  to  the  iron  or  steel  with  which 
it  has  been  used,  but  only  a  property  already  existing  there 
has  been  waked  up,  as  it  were,  or  developed.    It  is  not  possi- 
ble, by  any  means  known,  to  obtain  one  kind  of  polarity  with- 
out the  other  accompanying  it  at  the  same  time ;  that  is,  to 
obtain  a  north  pole  without  a  south  pole,  or  a  south  pole  with- 
out a  north  pole  accompanying  it  in  the  same  piece. 

516.  We  have  seen  above  that  a  piece  of  steel  may  be  mag- 
netized, or  an  artificial  magnet  produced,  simply  .by  bringing 
one  of  its  extremities  in  contact  with  one  of  the  poles  of  ano- 
ther magnet ;  but  it  will  be  better  to  pass  one  pole  of  a  magnet, 
held  in  an  inclined  position,  over  the  whole  length  of  the  steel 
bar,  each  time  moving  it  in  the  same  direction,  from  left  to 
right  or  from  right  to  left.     This  is  called  the  method  of  single 
touch;  the  design  of  passing  the  magnet  over  the  whole  bar  is 
to  prevent  the  formation  of  consecutive  points. 

In  the  method  by  double  touch,  as  it  is  called,  two  magnets 

are  used,  one  being  held  in 
each  hand;  and  the  north 
pole  of  one  being  brought 
near  the  south  pole  of  the 
other,  both  together  are 
placed  on  the  centre  of  the 
bar,  A  B,  to  be  magnetized, 
Fig.  246.  as  represented  in  figure  246, 

Quest.  514.  If  a  magnet  is  suddenly  broken  into  two  or  more  pieces,  will 
each  be  a  perfect  magnet  ?  515.  Does  a  magnet  lose  any  of  its  power  when 
it  is  used  to  induce  magnetism  in  a  bar  of  iron  or  steel  ?  Is  anything  com- 
municated to  the  body  magnetized  ?  What  is  the  method  of  magnetizing  a 
bar  of  steel  by  single  touch  ?  What  is  the  method  of  double  touch  ?  What 


MAGNETISM. 


263 


and  then  drawn  towards  its  extremities.  The  magnets  should 
always  be  held  considerably  inclined  to  the  bar  to  be  magnet- 
ized. This  process  should  be  repeated  ten  or  twelve  times, 
which  will  usually  be  sufficient  to  magnetize  the  bar  to  the 
highest  point. 

If  a  bar  of  steel  is  heated  to  redness,  and  then  suddenly 
cooled  by  throwing  water  upon  it  while  in  contact  with  one 
of  the  poles  of  a  magnet,  it  will  usually  be  found  to  become 
magnetic.  The  magnetism  is  induced  in  the  bar  while  in  its 
soft  state  by  reason  of  the  heat,  and  becomes  fixed  when  it  is 
hardened  by  cooling.  So  a  bar  of  steel  will  often  become 
feebly  magnetic  simply  by  being  hammered  while  lying  in  the 
direction  of  north  and  south,  or  by  being  struck  several  times 
with  a  hammer,  so  as  to  produce  a  ringing  sound. 

517.  The  poles  of  a  bar  magnet  are  so  far  apart 
that  it  is  inconvenient  to  bring  them  both  to  act 
on  the  same  object  at  once ;  artificial  magnets 
are  therefore  often  made  somewhat  in  the  shape 
of  a  horse-shoe,  as  seen  in  figure  247,  and  are 
called  horse-shoe  magnets.  A  piece  of  soft  iron, 
A  B,  used  to  connect  the  poles,  is  called  the  arma- 
ture^ or  keeper.  One  end  of  this  being  in  contact 
with  one  pole  of  the  magnet,  and  ttie  other  with 
the  other  pole,  it  will,  of  course,  become  power- 
fully magnetic,  and  will  be  attracted  with  great 
force.  By  attaching  weights  to  the  armature,  by 
means  of  a  cord,  the  magnet  may  in  this  way  be 
made  to  exert  the  greatest  power  of  which  it  is 
capable. 

By  combining  several  horse-shoe  magnets  pow- 
erful magnetic  batteries  have  sometimes  been  con- 
structed, of  sufficient  power  to  lift  many  pounds. 
The  several  magnets  are  placed  so  that  all  their 
north  poles  shall  be  in  contact,  and  all  their  south 
poles;  and,  as  a  matter  of  course,  they  react 
slightly  upon  each  other,  so  as  to  diminish  their 
joint  effect.  Thus,  if  there  are  six  magnets, 
each  of  which  alone  is  capable  of  lifting  four 
pounds,  the  six  together,  when  combined,  as  in 
figure  248,  will  not  lift  twenty-four  pounds. 

If  the  poles  of  a  powerful  horse- shoe  magnet  be 
placed  against  the  under  side  of  a  pane  of  glass  or  sheet  of 
paper  held  horizontally,  and  fine  iron-filings  be  sprinkled  upon 
the   upper  side,  they  will  arrange  themselves  in  a  peculiar 
* , 

other  method  is  described  ?  517.  What  is  the  form  of  the  horse-shoe  mag- 
net ?  What  is  the  armature,  or  keeper  ?  How  is  the  magnetic  battery  formed  ? 
Will  several  magnets  combined  in  this  manner  produce  a  joint  effect  equal 
to  the  sum  of  the  effects  of  the  single  magnets  ?  What  experiment  is  illus- 


Fig.  247. 


264  NATURAL     PHILOSOPHY. 

curve,  as  represented  in  figure 
249.  This  is  occasioned  by  the 
inductive  influence  of  the  two 
poles  of  the  magnet,  by  which 
all  the  small  pieces  of  iron  are 
converted  into  magnets,  which 
act  upon  each  other,  as  already 
explained  of  other  magnets. 
When  the  magnet  is  moved 
Fig.  249.  along  the  lower  surface  of  the 

glass  a  peculiar  movement  is 

produced  among  the  iron-filings,  not  unlike  that  of  a  multitude 

of  small  animals. 

518.  All  magnets,  if  left  to  themselves,  gradually  suffer  a 
diminution  of  their  magnetism,  and,  in  process  of  time,  even 
lose  it  entirely;   but  natural  magnets  retain  it  much  longer 
than  artificial  ones.     But  by  suitable  precautions  they  may  be 
preserved  for  any  length  of  time,  and  their  power  even   in- 
creased.   Two  magnets,  kept  with  their  similar  poles  together, 
injure  each  other  very  much,  and  if  nearly  of  equal  power,  may 
destroy  each  other  in  a  short  time :  if  one  is  much  stronger 
than  the  other,  the  weaker  will  be  likely  to  have  its  polarity 
reversed ;  that  is,  its  north  pole  will  become  a  south  pole,  and 
its  south  pole  a  north  pole. 

It  is  found  that  magnets  are  best  preserved  when  kept  con- 
stantly in  exercise.  This  is  accomplished  by  bringing  the 
unlike  poles  of  two  magnets  together,  as  by  placing  two  bar 
magnets  of  equal  length  side  by  side,  or  by  extending  a  piece 
of  soft  iron  from  one  pole  to  the  other.  The  power  of  the 
horse-shoe  magnet  will  often  be  considerably  increased,  in  a 
few  days,  by  suspending  from  its  armature  as  much  weight  as 
it  will  bear,  and  adding  to  it  from  time  to  time. 

Magnets  should  always  be  kept  free  from  rust,  which  im- 
pairs their  power;  and  they  should  also  be  protected  from 
mechanical  injury.  The  power  of  a  magnet  has  often  been 
greatly  impaired  by  a  single  blow,  or  by  a  fall  upon  the  floor 
or  pavement. 

519.  When  a  magnet  is  heated  to  redness  and  allowed  to 
cool  again,  its  magnetism  is  invariably  entirely  destroyed  ;  and 
its  power  is  impaired  by  even  so  small  a  degree  of  heat  as  that 
of  boiling  water.    On  the  other  hand,  at  very  low  tempera- 
tures the  power  is  increased. 

trated  in  figure  249  ?  518.  Does  the  power  of  a  magnet  diminish  by  keep- 
ing ?  What  precaution  may  be  taken  to  prevent  this  effect  ?  How  may  the 
power  of  a  magnet  be  increased  by  keeping?  What  is  said  of  the  effect  of 
a  blow  upon  a  magnet,  or  of  letting  it  fall  upon  the  pavement  ?  What  is 
said  of  the  effect  of  rust  upon  a  magnet  ?  519.  How  is  the  magnet  affected 
by  heat?  How  by  cold? 


MAGNETISM.  265 

520.  It  is  believed  that  nearly  all  substances  are  capable  of 
exhibiting  a  feeble  magnetism  when  under  the  inductive  influ- 
ence of  a  powerful  magnet ;  but  two  only,  (besides  iron  or  some 
of  its  compounds,)  the  metals  nickel  and  cobalt,  retain  it ;  and 
the  magnetism  of  these,  at  best,  is  very  weak. 

521.  Terrestrial  Magnetism.— We  have  seen  that  when  a 
natural  or  artificial  magnet  is  suspended  so  as  to  move  freely, 
it  will,  when  it  comes  to  a  state  of  rest,  present  one  of  its  poles 
to  the  north  and  the  other  to  the  south.     This  is,  no  doubt, 
produced  by  the  influence  of  the  earth  acting  as  an  immense 
but  distant  magnet  upon  the  needle.     Indeed,  in  order  to  un- 
derstand clearly  all  the-various  relations  of  the  magnetic  needle 
to  the  earth,  we  may  with  propriety  consider  the  latter  as  a 
great  magnet,  having  one  of  its  poles  at  or  near  the  north  pole 
of  the  earth,  and  the  other  pole  near  its  south  pole.     But  we 
have  concluded  to  call  that  pole  of  the  needle  which  points  to 
the  north  the  north  pole,  and  the  other  the  south  pole  (§  503) ; 
and  as  unlike  poles  attract  while  like  poles  repel  each  other,  it 
follows,  as  a  matter  of  course,  that  the  magnetic  pole  at  or 
near  the  north  pole  of  the  earth  must  be  a  south  pole,  or  pos- 
sess southern  polarity,  while  that  in  the  southern  hemisphere 
must  possess  north  polarity. 

522.  If  a  piece  of  steel,  made  in  the  form  of  the  magnetic 
needle,  is  accurately  balanced  upon  a  pivot,  so  as  to  remain  in 
a  horizontal  position,  after  being  magnetized  the  north  pole 
will  dip  or  be  depressed  considerably  below  its  former  hori- 
zontal position.    This  is,  no  doubt,  occasioned  by  the  influence 
of  the  earth's  magnetism,  which  is  exerted  more  on  the  north 

pole  than  on  the  south  pole,  so 
that  the  north  pole  is  drawn 
dowrrward.  This  is  not  sur- 
prising, since  we  are  situated 
so  much  nearer  the  north  than 
the  south  pole  of  the  earth. 
Let  AB,  figure  250,  be  a  bar 
magnet  lying  horizontally  upon 
the  table,  and  then  let  a  small 
.  magnet,  suspended  by  a  thread, 

so  as  to  hang  horizontally,  be 
held  at  D,  over  the  centre  of  the  large  magnet ;  its  north  pole 

Quest.  520.  Is  it  supposed  that  nearly  all  substances  are  capable  of  ex- 
hibiting slight  traces  of  magnetism  when  under  the  influence  of  a  powerful 
magnet  ?  What  two  only,  besides  iron  and  its  compounds,  retain  the  mag- 
netism ?  521.  What  is  it  that  occasions  the  magnetic  needle  to  settle  in  a 
north  and  south  direction  ?  May  we  consider  the  earth  to  act  as  a  great 
magnet  upon  magnetized  bodies  at  its  surface  ?  What  kind  of  polarity  must 
its  pole  in  the  northern  hemisphere  possess  ?  How  does  this  appear  ?  522. 
If  a  piece  of  steel  is  accurately  balanced  upon  a  pivot,  and  then  magnetized, 
what  effect  is  observed  ?  How  is  this  accounted  for  ?  How  is  it  illustrated 
in  figure  250  ? 

23 


i 


NATURAL      PHILOSOPHY. 

wilJ  point  towards  B  and  its  south  pole  towards  A;  both  of"  its 
poles  being  equally  acted  upon  by  the  poles  of  the  large  mag- 
net, it  will  remain  in  its  horizontal  position,  as  shown  in  the 
figure.  But  let  it  next  be  carried  gradually  towards  the  north 
pole,  A,  of  the  magnet ;  the  south  pole  of  the  small  needle  will 
immediately  begin  to  dip,  and  the  dip  will  increase  as  it  ap- 
proaches the  pole  A.  So,  if  the  needle  is  moved  towards  the 
other  pole  of  the  magnetic  bar,  the  other  pole  will  be  depressed 
in  the  same  manner.  The  position  it  would  take  at  C  and  E 
is  shown  in  the  figure. 

523.  A  needle  prepared  expressly  for  showing  the  dip  or 
variation  from  a  horizontal  position  is  called  a  dipping-needle. 

Figure  251  represents  the  sim- 
plest form  of  this  instrument. 
A  B  is  a  flat  piece  of  wood,  for 
a  base,  provided  with  a  spirit- 
level  and  screw,  for  leveling  it 
with  great  accuracy ;  and  to  it 
is  attached  a  graduated  circle 
of  metal,  C  C,  having  on  each 
side  of  it  a  horizontal  bar,  H  H, 
to  support  the  needle,  N  S,  so 
that  it  revolves  freely  in  a  ver- 
tical circle  between  them.  As 
the  parts  of  the  needle  are  made 
to  balance  each  other  very  ac- 
curately before  it  is  magnet- 
ized,  the  position  it  takes  after 
becoming  a  magnet  will  de- 
pend upon  the  magnetic  attraction  of  the  earth. 

524.  By  this  instrument  it  has  been  determined  that  near  the 
equator  the  needle  is  horizontal ;  but  as  it  is  carried  north  the 
north  pole  begins  to  dip,  while  at  the  south  of  the  equator  the 
south  pole  of  the  needle  dips.     Towards  the  polar  regions, 
either  in  the  northern  or  southern  hemisphere,  the  dip  becomes 
very  great ;  and  if  the  true  pole  of  the  earth  could  be  found, 
the  needle  would  there  stand  perpendicularly.     The  dip  of  the 
needle  at  any  place  is  found  to  be  subject  to  a  slight  variation ; 
but  in  London,  in  1830,  it  was  69°  38';  at  Paris,  in  1835,  it  was 
67°  24'.    The  dip,  at  the  present  time,  is, 

At  Baltimore,          about 71°  30> 

"   Philadelphia,          "     72    15 

"   New  York,  «     73     0 

"   Middletown,  Ct.,  "     73   30 

"   Boston,  »     74   24 

Quest.  523.  What  is  the  dipping-needle  ?  524.  What  is  the  dip  at  the 
equator  ?  What  is  the  effect  if  the  needle  is  removed  to  the  north  or  south 
of  the  equator  ?  What  is  the  amount  of  the  dip,  at  the  present  time,  at 
Baltimore,  New  York,  and  Boston  ? 


MAGNETISM.  267 

525.  We  have  said  that  near  the  equator  there  is  no  dip ;  the 
places  where  this  occurs  are  situated  in  a  line  that  encircles 
the  earth,  and  is  called  the  magnetic  equator.    It  deviates  much 
from  the  geographical  equator,  being  sometimes  north  and 
sometimes  south  of  it,  and,  of  course,  crossing  it  several  times. 

526.  It  has  been  stated,  also,  that  the  magnetic  needle,  when 
properly  suspended,  and  uninfluenced  by  any  other  magnet- 
ized body,  will  settle  in  the  general  direction  of  north  and 
south ;  but  it  is  now  well  known  that  it  is  subject  to  deviate 
more  or  less  to  the  east  or  west  of  this  position.     This  devia- 
tion of  the  needle  from  the  true  meridian  is  called  its  declina- 
tion, or  variation,  and  sometimes  amounts  to  many  degrees. 

The  direction  in  which  the  needle  settles  in  any  place  is 
called  the  magnetic  meridian  of  the  place ;  and  the  angle  be- 
tween this  and  the  true  meridian  is,  of  course,  the  variation. 

The  variation  at  any  place  is  constantly  changing :  at  Lon- 
don, about  265  years  ago,  it  was  1 1°  15'  east ;  that  is,  the  north 
pole  of  the  needle  deviated  11  degrees  15  minutes  to  the  east 
of  the  true  north ;  but  it  gradually  diminished,  so  that,  in  80 
years  afterwards,  or  about  the  year  1660,  it  became  nothing, 
and  the  needle  pointed  to  the  true  north.  Immediately  after- 
wards a  western  declination  commenced,  which  gradually  and 
uniformly  increased  until  1815,  when  it  amounted  to  24°  27': 
since  that  time  it  seems  to  have  been  diminishing,  and  in  1840 
was  said  to  be  less  than  24  degrees.  At  Philadelphia  the  va- 
riation in  1840  was  about  3°  52'  west;  at  New  York  about 
5°  23';  at  New  Haven,  Ct,  about  6°  0';  at  Middletown,  Ct, 
about  6°  40',  and  at  Boston  about  8°  55'.  The  variation  at  all 
these  places,  it  is  believed,  is  now  diminishing.  The  line  of 
no  variation  is  an  irregular  circle,  passing  round  the  earth 
from  north  to  south ;  in  this  country,  at  the  present  time,  it 
passes  through  lake  Huron  and  lake  Erie,  a  little  west  of  the 
western  line  of  Pennsylvania,  crosses  the  south-west  corner 
of  that  state,  and  the  states  of  Virginia  and  North  Carolina, 
entering  the  Atlantic  ocean  a  little  east  of  the  line  between 
North  and  South  Carolina.  This  line  of  no  variation  is  by  no 
means  fixed,  but  is  constantly  varying,  sometimes  moving 
gradually  east  for  a  series  of  years,  and  then  again  changing 
its  motion  to  the  west.  East  of  this  line,  for  a  considerable 
distance,  the  variation  is  west,  but  west  of  it  the  variation  is 
east ;  and  on  both  sides  it  is  greater  the  farther  the  distance, 
within  certain  limits,  from  the  line. 


Quest.  525.  What  is  the  magnetic  equator  ?  Does  it  deviate  from  the 
geographical  equator?  526.  Does  ihe  needle  always  point  to  the  true  north 
and  south  ?  What  is  meant  by  the  declination  or  variation  of  the  needle  ? 
What  is  the  magnetic  meridian  of  a  place  ?  Is  the  declination  at  any  place 
always  the  same  ?  What  changes  have  taken  place  in  the  declination  at 
London  in  the  last  265  years?  What  is  the  present  declination  at  New 
York  ?  What  is  meant  by  the  line  of  no  variation  ?  Through  what  parts 
of  this  country  does  (his  line  pass  ?  What  is  said  of  the  variation  east  and 
west  of  this  line  ? 


268  NATURAL     PHILOSOPHY. 

527.  Both  the  declination  and  the  dip  of  the  magnetic  needle 
are  subject  to  a  variation  according  to  the  season  of  the  year 
and  the  hour  of  the  day.    In  this  country  the  declination  of  the 
needle  from  the  true  north  is  greater  in  the  middle  of  the  day 
than  in  the  night;  and  this  diurnal  change  is  greater  in  the 
warm  months  of  summer  than  in  the  winter. 

528.  We  are  now  prepared  to  investigate  a  little  more  parti- 
cularly the  relation  of  the  earth,  considered  as  a  great  magnet, 
and  small  magnets  at  any  place  upon  its  surface."  In  the  north- 
ern hemisphere,  especially  in  high  latitudes,  the  pole  near  the 
north  geographical  pole  of  the  earth  is  much  nearer  to  us  than 
the  other  magnetic  pole,  and  it  is  its  influence,  therefore,  which 
is  chiefly  to  be  noted.     But  this  pole  of  the  earth  is  a  south 
pole — as  we  have  seen  (§  521) — that  is,  it  possesses  southern 
polarity,  and  therefore  it  draws  towards  it  the  north  pole  of 
the  needle. 

But,  if  the  earth  may  with  propriety  be  considered  an  im- 
mense magnet,  acting  like  other  magnets,  we  may,  of  course, 
expect  it  to  have  an  inductive  influence,  as  well  as  other  mag- 
nets, on  masses  of  iron  and  steel.  And  this  is  found  to  be  the 
case.  Bars  of  steel  that  have  stood  long  in  a  perpendicular 
position,  and  even  bars  of  common  iron,  are  often  found  to 
have  acquired  a  feeble  degree  of  magnetism,  the  lower  end 
being  a  north  and  the  upper  end  a  south  pole.  Tongs  and 
pokers,  from  their  having  some  degree  of  hardness,  and  their 
being  almost  always  kept  nearly  perpendicular,  are  generally 
magnetic,  as  will  be  seen  by  presenting  the  lower  extremity 
very  cautiously  to  the  north  pole  of  a  needle,  or  the  upper  end 
to  the  south  pole.  In  either  case  slight  repulsion  will  be  pro- 
duced, which  indicates  the  presence  of  similar  poles  The 
blade  of  a  penknife  may  often  be  magnetized  by  a  pair  of 
tongs,  or  a  poker,  so  as  to  be  capable  of  lifting  a  large  sewing- 
needle. 

529.  The  inductive  influence  of  the  earth's  magnetism  may, 
therefore,  be  made  use  of  to  obtain  permanent  magnetism,  in 
the  absence  of  all  other  magnetized  bodies.     This  is  best  ac- 
complished as  follows: — Let  the  small  piece  of  steel  to  be  mag- 
netized be  suspended  by  threads  to  the  edge  of  a  table,  in  a 
north  and  south  position,  and  then  let  two  long  bars  of  iron, 
as  two  pokers,  be  held,  one  above  it  and  the  other  below  it,  at 

Quest.  527.  Do  both  the  variation  and  dip  of  the  needle  have  a  daily 
change  ?  528.  Which  of  the  poles  of  the  earth  is  nearest  to  us  ?  If  the 
earth  may  be  considered  as  a  great  magnet,  should  we  expect  it  to  exert  an 
inductive  influence  upon  masses  of  iron  or  steel  upon  its  surface  ?  What 
effect  is  produced  upon  bars  of  steel  that  have  stood  long  in  a  perpendicular 
position?  Which  extremity  is  a  north  pole?  How  is  this  accounted  for? 
Why  are  tongs  and  pokers  usually  found  to  be  magnetic  ?  How  may  they 
be  made  to  magnetize  the  blade  of  a  penknife?  529.  How  may  the  inductive 
influence  of  the  earth's  magnetism  be  made  use  of  to  obtain  permanent  mag- 


MAG  N  ETISML 


269 


Fig.  252. 


its  centre,  as  is  shown  in  A, 
figure  252.  The  upper  bar  is 
now  to  be  carried  to  the  south, 
and  the  lower  bar  to  the  north, 
as  shown  in  B,  both  being  kept 
in  a  vertical  position ;  after  re- 
peating this  several  times,  the 
piece  of  steel  will  generally  be 
found  to  be  fully  magnetized. 
After  what  has  been  said,  any 
further  explanation  is  hardly 
necessary.  The  bars  of  iron, 
by  the  inductive  influence  of 
earth,  become  magnetic,  their 
lower  ends  being  north  poles 
(§521),  and,  by  using  two  at 
the  same  time,  in  the  manner 
described,  the  effect  is  much  in- 
creased. By  placing  the  piece 
of  steel  to  be  magnetized  in  a 
north  and  south  direction,  the 
direct  inductive  influence  of  the 


earth  upon  it  favours  the  action  of  the  iron  bars. 

530.  The  compass  is  an  instrument  fitted  up  with  a  magnetic 
needle  and  a  graduated  circle  of  metal,  or  a  circular  card,  for 
the  purpose  of  measuring  the  angles  any  objects  make  with 
the  meridian.     The  mariner's  compass  usually  has  the  needle 
attached  to  a  circular  card,  which  is  suspended  upon  a  pivot, 
and  turns  freely.     When  great  accuracy  is  required,  it  is  evi- 
dent, allowance  must  be  made  for  the  declination  of  the  needle 
at  the  place;  this  is  especially  important  for  seamen,  whose 
only  guide  across  the  pathless  ocean  is  the  faithful  needle.    So, 
also,  local  attractions  often  produce  great  derangement,  as  the 
vicinity  of  masses  of  iron,  or  iron  mines,  which  must  always 
be  guarded  against.     The  iron  used  in  the  construction  of 
ships  often  produces  a  considerable  derangement  of  the  needle, 
and  means  have  been  devised  to  apply  the  necessary  correc- 
tion ;  but  the  subject  is  too  complicated  to  be  here  introduced. 

531.  As  the  natural  magnet,  or  loadstone,  is  only  an  oxide 
of  iron  possessing  the  magnetic  property,  it  is  evident  this  pro- 
perty has  been  communicated  to  it  by  the  inductive  influence 
of  the  earth ;  and  if  masses  of  it  were  examined  as  they  lie  in 

netism  ?  What  is  the  explanation  of  this  process  ?  530.  What  is  the  com- 
pass ?  How  is  the  mariner's  compass  usually  constructed  ?  In  the  use  of 
the  compass  must  allowance  always  be  made  for  the  variation  of  the  needle  f 
Dp  local  attractions  sometimes  affect  the  action  of  the  compass?  What  is 
said  of  the  action  of  the  iron  used  in  the  construction  of  ships  upon  the  com- 
pass? 531.  How  are  we  to  suppose  the  magnetic  virtue  has  been  commu- 
nicated to  the  masses  of  iron  ore  existing  in  the  earth  ? 
23* 


270  NATURAL     PHILOSOPHY. 

the  earth,  the  situation  of  the  poles  would,  no  doubt,  confirm 
this  remark. 

532.  Theories  of  Magnetism. — Various  theories  have,  at  different  times, 
been  proposed  to  account  for  the  phenomena  of  magnetism,  but  with  little 
success.     So  far  as  any  theory  on  the  subject  is  now  adopted,  that  which 
supposes  there  are  two  magnetic  fluids,  a  Boreal  and  an  Austral,  to  the 
agency  of  which  all  magnetic  phenomena  are  to  be  attributed,  seems  ge- 
nerally to  prevail.     These  fluids,  it  is  supposed,  naturally  reside  in  the 
particles  of  iron  and  other  substances  that  are  capable  of  becoming  mag- 
netic, in  a  state  of  combination.     The  particles  of  each  of  these  fluids  are 
supposed  to  attract  those  of  the  other,  but  repel  those  of  the  same  kind. 
When  these  two  fluids  are  in  a  state  of  combination  they  are  entirely  neu- 
tral, but  become  active  when  separated.     This  separation  of  the  united 
fluids  is  produced  by  the  inductive  influence  of  either  the  one  or  the  other 
acting  alone,  constituting  the  pole  of  another  magnet.     In  soft  iron,  as 
soon  as  the  influence  which  produced  the  separation  is  removed,  the  par- 
ticles of  the  two  fluids  again  unite,  and  the  magnetic  phenomena  disap- 
pear ;  but  in  hardened  steel  and  the  magnetic  oxide  of  iron,  and,  indeed, 
in  all  other  substances  which  may  become  permanently  magnetic,  they 
are  supposed  to  remain  separate. 

533.  But,  though  these  fluids  are  thus  separated,  we  are  not  to  suppose 
that  they  are  ever  transported  from  one  body  to  another,  or  even  from  one 
part  to  another  of  the  same  piece  of  iron  or  steel.     We  have  heretofore 
seen  (§514)  that  when  a  bar  magnet  is  broken  into  two  pieces,  in  the 
centre,  we  do  not  have  a  north  pole  in  one  and  a  south  pole  in  the  other, 
as  would  be  the  case  if  the  two  fluids  were  separated  in  the  opposite  ex- 
tremities of  the  bar,  Irjt  each  piece  is  found  to  be  a  perfect  magnet,  having 
both  a  north  and  a  south  pole,  precisely  like  the  bar  before  it  was  broken. 
We  must  therefore  suppose  the  two  fluids  are  never  separated  from  the 
particle  to  which  they  belong,  but  are  only  removed  to  opposite  sides  of 

the  particle,  as  shown  in  figure  253.  Let 
SN  be  a  bar  magnet  consisting  of  two 
rows  of  particles,  the  austral  fluid  will  all 
be  collected  on  the  sides  of  the  particles 
towards  N,  as  shown  by  the  letter  n,  and 


Fig.  253.  the  boreal  on  the  sides  next  to  S,  as  shown 

by  the  letter  s.  The  effect  of  thus  sepa- 
rating the  two  fluids,  in  connection  with  the  particles  of  a  piece  of  iron  or 
steel,  is  to  develop  in  it  the  ordinary  properties  of  magnetism. 

534.  It  is  known  that  in  the  centre  of  a  magnet,  that  is,  at  a  point 
equally  distant  from  the  two  extremities,  there  is  no  attractive  influence ; 
but  at  a  little  distance  from  this  point,  towards  either  end,  it  begins  to 
appear,  and  increases  quite  to  the  ends  called  the  poles.  The  reason  of 
this  is  evident,  if  our  theory  is  true,  for,  except  the  extreme  particles,  each 
north  pole  is  always  in  contact  with  a  south  pole,  and  of  course  the  two 
should  neutralize  each  other,  so  that  the  attractive  influence  is  exerted 
only  by  the  extreme  particles,  and  extends  to  a  certain  distance  from 
them  in  every  direction.  The  influence  of  each  pole  will  therefore  be 
neutralized  at  the  central  point  between  them. 

For  a  full  discussion  of  the  intimate  relation  between  this  branch  of 
science  and  that  of  electricity,  see  author's  Chemistry. 


ELECTRICITY.  271 

CHAPTER   VIII. 
ELECTRICITY. 

535.  IF  a  glass  rod,  or  tube,  that  has  remained  untouched 
for  some  time,  be  held  near  a  feather  or  other  light  body,  sus- 
pended by  a  fine  silk  thread,  nothing  special  is  observed,  though 
the  glass"  be  presented  so  near  as  to  touch  it,  and  then  with- 
drawn; the  feather  maintains  its  position  undisturbed.     But 
let  the  glass  tube  be  made  dry  and  warm,  and  then  rubbed 
briskly  for  a  few  seconds  with  a  woollen  cloth  or  a  silk  hand- 
kerchief; upon  holding  it  near  the  feather  now  it  is  at  once 
disturbed,  even  when  the  tube  is  at  some  distance,  and  mani- 
festly tends  to  approach  it ;  and  when  the  tube  is  brought  suf- 
ficiently near,  it  suddenly  darts  to  it,  usually  adhering  for  a 
moment,  when  it  is  repelled  with  equal  force. 

536.  It  is  evident  that,  by  means  of  the  friction  with  the  cloth 
or  handkerchief,  a  property  has  been  imparted  to  the  glass 
which  it  did  not  before  possess,  and  by  virtue  of  which  it 
exerts  an  attraction  upon  the  feather.    But  this  property  is  not 
peculiar  to  glass;  pieces  of  resin,  sealing-wax,  amber,  sulphur, 
&c.,  when  rubbed  in  a  similar  manner,  possess  the  same  power 
of  attracting  other  light  bodies. 

The  physical  agent,  whatever  its  nature  may  be,  which  is 
thus  called  into  operation,  in  these  and  other  substances,  by 
friction,  and  to  which  the  attractions  are  to  be  attributed,  is 
called  Electricity.  This  name  is  derived  from  electron,  the 
Greek  name  for  amber,  the  first  substance  which  was  observed 
to  exhibit  the  phenomena  of  attrac- 
tion just  described.  The  first  obser- 
vations on  the  subject  that  are  on 
record  were  made  by  Thales,  about 
600  years  before  the  birth  of  Christ. 
537.  To  examine  the  various  cir- 
cumstances attending  the  pheno- 
mena above  described,  let  a  glass 
tube  an  inch  in  diameter  and  two 
feet  long  be  provided,  and  also  a 
stick  of  sealing-wax  an  inch  in  di- 
ameter and  12  or  14  inches  long,  and 
Fig.  254.  a  pith-ball  electrometer,  figure  254. 

Quest.  535.  If  a  dry  glass  tube  is  rubbed  with  a  woollen  cloth  or  silk 
kand kerchief,  and  then  held  near  a  feather  or  other  light  body,  what  is  the 
effect  ?  If  the  feather  is  allowed  to  touch  the  tube,  what  is  the  result  ? 
536.  What  other  substances  are  mentioned  as  possessing  the  same  property 
after  being  rubbed?  To  what  agent  are  these  attractions  and  repulsions 
attributed  ?  From  what  is  the  name  electricity  derived  ?  537.  What  three 
pieces  of  apparatus  are  recommended  for  pursuing  our  investigation  in  this 


272 


NATURAL     PHILOSOPHY. 


This  electrometer,  or  measurer  of  electricity,  consists  of  a  glass 
rod,  A,  fixed  in  a  stand,  and  bent  at  top,  so  that  a  ball,  B,  made 
of  the  pith  of  the  elder,  may  be  suspended  from  it  by  a  thread 
of  silk.  On  rubbing  the  tube  or  sealing-wax  with  a  warm  and 
dry  woollen  cloth  or  silk  handkerchief,  and  presenting  it  near 
the  pith-ball,  as  at  C,  the  ball  is  strongly  attracted  towards  it, 
as  to  D,  and,  if  not  allowed  to  touch  the  tube,  remains  there 
until  the  glass  or  sealing-wax  is  moved.. 

When  a  body  is  capable  of  producing  this  effect,  it  is  said  to 
be  excited,  and  the  result  with  the  pith-ball  is  the  same  whether 
an  excited  glass  tube  be  used  or  an  excited  stick  of  sealing- 
wax,  provided  the  ball  is  not  allowed  to  come  in  contact 
with  it. 

When  using  the  excited  glass  tube, 
A,  figure  255,  if  the  pith-ball,  B,  is  al- 
lowed to  touch  it,  it  at  once  flies  off,  as 
to  C,  and  remains  there  until  the  tube 
is  removed,  constantly  manifesting  a 
strong  repulsion  for  it.  If  the  finger  is 
now  touched  to  the  ball,  and  then  the 
same  experiment  repeated  with  the 
stick  of  sealing-wax,  the  results  will  be 
precisely  the  same;  the  pith-ball  will 
at  first  be  attracted,  but  after  contact 
it  will  be  as  strongly  repelled. 

538.  Thus  far,  then,  we  have  ob- 
served no  difference  between  the  action 
of  the  glass  tube  and  that  of  the  sealing-wax ;  both  seem  to 
have  the  same  properties,  both  attracting  the  pith-ball,  and 
then,  after  contact,  repelling  it.  But,  having  excited  the  glass 
tube,  let  us  now  present  it  to  the  pith-ball ;  as  before,  it  is  at- 
tracted to  the  glass  until  coming  in  contact  with  it,  when  it  is 
repelled.  Next,  let  the  sealing-wax  be  quickly  excited,  and 
presented  to  the  pith-ball ;  a  strong  attraction  ensues :  but  if 
the  sealing-wax  is  removed,  and  the  tube  again  presented,  it 
is  repelled  as  before. 

If  we  had  commenced  with  the  sealing-wax,  exciting  it  and 
bringing  it  in  contact  with  the  ball,  and  then  presented  the 
excited  glass  tube,  the  phenomena  observed  would  have  been 
the  same ;  and  we  therefore  find  that  when  the  excited  glass 

subject  ?  What  is  an  electrometer  ?  When  is  a  body  said  to  be  excited  ?  If 
the  pith-ball  is  not  allowed  to  touch  the  glass  or  sealing-wax,  will  the  result 
be  the  same  with  both  ?  If  the  pith-ball  is  allowed  to  touch  the  excited  tube, 
what  will  be  the  effect  ?  538.  So  far  as  we  have  now  pursued  our  investi- 
gation, has  any  difference  been  observed  between  the  action  of  the  tube  and 
that  of  the  sealing-wax  ?  But  if  we  bring  the  excited  tube  in  contact  with 
the  pith-ball,  so  as  to  cause  it  to  be  repelled,  and  then  present  the  excited 
sealing-wax,  what  is  the  effect  ?  If  we  had  commenced  with  the  excited 
sealing-wax,  touching  the  ball  with  it,  and  then  presented  the  excited  tube, 
would  the  result  have  been  the  same  ?  If  two  pith-balls  are  suspended  from 


Fig.  255. 


ELECTRICITY.  273 

tube  attracts  the  pith-ball,  the  excited  sealing-wax  repels  it ; 
and  when  the  sealing-wax  repels,  the  glass  attracts. 

If,  now,  two  pith-balls  be  suspended  from  the  same  support 
by  silk  threads,  so  as  to  rest  in  contact,  when  the  excited  glass 
tube  is  brought  near  they  will  be  attracted,  as  before,  and  then 
repelled  ;  but  when  the  tube  is  withdrawn  it  will  be  found  they 
no  longer  fall  into  the  vertical  position ;  but,  on  the  contrary, 
_-^  they  repel  each  other,  causing  the  threads 

**"    ^y  by  which  they  are  suspended  to  diverge,  as 

P.  A  and  B,  figure  256.     If  the  stick  of  sealing- 

X  wax  had  been  used,  the  same  effect  would 

/  \          have  been  produced. 

/     \  539.  By  the  above  experiments  the  fol- 

I       \       lowing  facts,  it  would  seem,  may  be  consi- 
/         \      dered  as  settled : — 

L        B\         1.  By  the  friction  of  the  dry  woollen 
r\  /K  cloth  or  silk  handkerchief  a  quality  is  im- 

^  parted  to  the  glass  and  the  sealing-wax,  by 
virtue  of  which  they  become  capable  of  ex- 
-25G  erting  an  attraction  on  the  suspended  pith- 

ball. 

2.  After  coming  in  contact  with  the  excited  glass  or  wax 
the  state  of  the  ball  is  changed,  so  that,  instead  of  being  at- 
tracted by  the  glass  or  wax  it  has  just  touched,  it  is  repelled. 

3.  When  the  pith-ball  has  once  been  in  contact  with  the  ex- 
cited glass,  and  is  repelled  by  it,  it  will  be  attracted  by  the 
excited  wax;   so,  also,  after  it  has  been  in  contact  with  the 
excited  wax,  and  is  repelled  by  it,  it  will  be  attracted  by  the 
excited  glass. 

4.  When  two  pith  balls  have  been  brought  in  contact,  either 
with  the  excited  glass  or  sealing-wax,  so  as  to  be  repelled  by 
it,  they  also  repel  each  other. 

540.  To  account  for  these  phenomena,  and  explain  them,  the 
two  following  theories  have  been  proposed : — 

The  theory  first  proposed  is  that  usually  ascribed  to  Dufay, 
and  therefore  called  Dufay's  theory ;  the  other  was  proposed 
by  Franklin,  and  is  therefore  called  Franklin's  theory. 

541.  The  theory  of  Dufay  supposes  that  all  bodies  in  nature, 
in  their  natural  state,  always  have  in  combination  with  their 
particles  two  fluids,  which,  however,  so  attract  and  neutralize 
each  other,  as  to  be  entirely  concealed.    It  supposes,  also,  that 
though  each  fluid  strongly  attracts  the  other,  yet  the  particles 
of  the  same  fluid  are  mutually  repulsive,  and  tend  to  diffuse 
themselves  when  unobstructed.     When  the  two  fluids  are  in 

the  same  support,  and  then  touched  with  the  excited  tube  or  sealing-wax, 
what  will  be  the  effect  ?  539.  What  are  some  of  the  conclusions  arrived  at 
by  the  preceding  experiments  ?  540.  What  two  theories  have  been  pro- 
posed to  account  for  the  phenomena  of  electricity  ?  541.  How  many  fluids 
does  the  theory  of  Dufay  suppose  all  bodies  to  have  in  combination  with 
them  in  their  natural  state  ?  What  is  supposed  to  be  the  state  of  a  body,  on 


274  NATURAL     PHILOSOPHY. 

a  state  ot  combination  in  a  body,  no  indications  of  either  are 
perceived ;  but  when,  by  any  means,  they  are  separated,  and 
either  of  them  accumulated  in  a  body,  that  body  is  said  to  be 
excited,  and  exhibits  the  various  phenomena  of  electricity 
which  have  been  described. 

One  of  the  most  common  means  of  separating  the  two  fluids 
is  by  friction,  as  above  described,  when  one  or  the  other  of 
them  accumulates  in  the  body  which  is  rubbed,  and  there  mani- 
fests its  peculiar  properties.  That  fluid  which  usually  collects 
on  glass  and  other  vitreous  substances  by  friction  is  called  the 
vitreous  Jluid,  while  that  which  is  developed  on  sealing-wax 
and  other  resinous  substances  is  called  the  resinous  fluid. 

542.  The  other  theory,  that  of  Franklin,  supposes  that  there 
is  in  nature  a  single  electric  fluid  only,  the  particles  of  which 
repel  each  other,  but  attract  and  are  attracted  by  all  other 
bodies.     It  supposes  that  all  bodies,  in  their  natural  state,  in 
which  they  exhibit  no  signs  of  electricity,  contain  a  portion  of 
this  fluid,  called  their  natural  share;  and  that,  when  they  are 
excited,  they  are  made  to  contain  either  more  or  less  than  their 
natural  share.     When  a  piece  of  glass  is  rubbed,  a  portion  of 
this  fluid  is  supposed  to  pass  from  the  substance  used  as  a  rub- 
ber to  the  glass,  which,  therefore,  is  made  to  contain  more  than 
its  natural  share,  and  is  said  to  be  positively  electrified.    On  the 
other  hand,  when  a  stick  of  sealing-wax,  or  other  resinous  sub- 
stance, is  rubbed,  a  portion  of  the  fluid  contained  in  it  is  sup- 
posed to  escape  to  the  rubber,  leaving  in  the  wax,  of  course, 
less  than  its  natural  share;  and  it  is  therefore  said  to  be  nega- 
tively electrified. 

543.  It  will  be  seen,  therefore,  that  the  positive  electricity  of 
Franklin's  theory  corresponds  to  the  vitreous  of  Dufay's  the- 
ory, and  the  negative  of  the  former  to  the  resinous  of  the  latter. 

Dufay's  theory  of  two  fluids  is  now  more  generally  received 
than  that  of  Franklin,  though  the  terms  positive  and  negative 
are  universally  used  to  designate  the  two  fluids,  in  preference 
to  the  terms  vitreous  and  resinous.  But  though  Dufay's  theory 
is  now  most  generally  received,  there  are  those  who  believe 
that  all  electrical  phenomena  may  equally  as  well  be  explained 
by  that  of  Franklin. 

544.  By  referring  now  to  the  experiments  above  described 
(§  537)  it  will  be  seen  that  when  two  substances  are  similarly 
electrified — that  is,  when  they  are  both  excited  either  positively 

this  theory,  when  it  is  excited  ?  What  is  the  fluid  called  which  usually  col- 
lects upon  glass  when  it  is  rubbed  ?  What  is  the  other  called,  which  col- 
lects upon  sealing-wax  by  friction  ?  542.  How  many  fluids  does  Franklin's 
theory  suppose  to  be  contained  in  bodies  in  their  natural  state  ?  When  a 
piece  of  glass  is  rubbed,  what  is  supposed  to  be  the  effect  on  this  fluid  ? 
What  is  the  effect  of  friction  on  sealing-wax  ?  What  terms  are  used  to  indi- 
cate the  state  of  the  glass  and  of  the  sealing-wax  after  being  excited  ?  543. 
What  terms  in  the  two  theories  correspond  in  meaning  ?  Which  of  these 
theories  is  now  most  generally  received  ?  544.  When  do  two  bodies  attract 


ELECTRICITY.  275 

• 

or  negatively — they  repel  each  other;  but  when  oppositely 
electrified — that  is,  when  one  is  positive  and  the  other  nega- 
tive— they  attract  each  other. 

545.  By  experiment  it  is  found  that  while  electricity  passes 
freely  over  some  bodies,  it  refuses  to  pass  over  others,  or  passes 
over  them  with  difficulty.     The  former  are  called  conductors 
and  the  latter  non-conductors. 

The  metals  are  usually  considered  the  best  conductors ;  and 
after  these  we  may  reckon  charcoal,  solution  of  salt,  water,  and 
living  animals. 

The  following  are  some  of  the  most  important  non-conduct- 
ors, viz: — gum  lac,  amber,  sealing-wax,  sulphur,  glass,  silk, 
feathers,  dry  air,  baked  wood,  and  oils. 

Though  many  experiments  have  been  made  to  determine 
why  some  bodies  conduct  electricity  while  others  will  not,  yet 
it  still  remains  entirely  unknown.  All  we  can  say  with  regard 
to  this  property  of  bodies  is,  that  such  is  their  nature. 

546.  When  a  body  is  surrounded  entirely  by  non-conductors 
it  is  said  to  be  insulated.    Usually  this  is  accomplished  by  sup- 
porting the  body,  whatever  it  is,  upon  glass  pillars,  or  suspend- 
ing it  by  threads  of  silk.     As  the  air,  when  dry,  is  a  non- 
conductor, a  very  little  only  of  the  fluid  will  be  conveyed  away 
by  it;  but  when  it  is  saturated  with  moisture,  as  it  usually  is 
in  warm  weather,  it  becomes  a  tolerably  good  conductor,  and 
conveys  the  fluid  away  rapidly ;  so  that  electrical  experiments, 
at  such  times,  succeed  only  with  great  difficulty. 

547.  If  we  again  refer  to  the  bodies  which  were  used  in  per- 
forming the  experiments  with  the  pith-balls  (§  536—539),  it  will 
be  seen  they  are  all  non-conductors ;  and  but  for  this  property 
the  fluid,  as  it  was  excited,  would  have  been  conveyed  away 
to  the  earth,  and  failed  to  make  itself  manifest  in  the  manner 
we  have  seen.     Hence  it  is  that  only  non-conductors  usually 
become  electrical  by  friction ;  but  conductors  may  also  be  ex- 
cited by  friction,  provided  they  are  first  insulated.     Thus,  if  a 
piece  of  iron,  which  is  a  conductor,  be  supported  on  glass  pil- 
lars, in  a  dry  atmosphere,  and  struck  several  times  with  a  cat's 
skin,  it  will  be  found  to  be  feebly  excited. 

548.  When  an  excited  body  is  held  in  a  dark  place — or,  bet- 
ter, when  a  body,  as  a  glass  tube,  is  excited  in  a  dark  room — 
faint  flashes  of  light  will  be  seen  upon  its  surface,  accompanied 
by  a  crackling  noise.    If  the  body  is  perfectly  electrified,  as 

and  when  do  they  repel  each  other  ?  545.  Will  electricity  pass  with  equal 
facility  over  the  surfaces  of  all  bodies  ?  Into  what  two  classes  are  bodies 
divided  in  reference  to  their  conducting  power  ?  What  are  some  of  the  best 
conductors?  What  are  some  of  the  principal  non-conductors  ?  546.  When 
is  a  body  said  to  be  insulated  ?  How  is  this  usually  accomplished  ?  Why 
do  electrical  experiments  succeed  only  with  difficulty  in  a  moist  atmosphere  ? 
547.  Why  do  non-conducting  substances  only  usually  become  excited  by 
friction  ?  How  may  a  piece  of  iron,  which  is  a  conductor,  be  excited  ?  548. 
What  is  observed  when  a  glass  tube  is  excited  in  a  dark  room  ?  If  a  pointed 


276  NATURAL     PHILOSOPHY. 

when  the  glass  tube  is  used,  and  a  pointed  wire  or  needJe  be 
presented  to  it,  a  bright  spark  will  be  seen  upon  its  point,  as 

represented  at  B,  figure  257. 
If  the  body  is  negatively 
electrified,  and  a  pointed 
wire  be  presented  to  it,  a 
luminous  brush  will  appear 
on  its  point,  as  shown  on  A. 
In  the  first  case  we  may 

suppose  the  positive  fluid 

Fi    257  to   be   passing  on   at  the 

point,  or  the  negative  fluid 
to  be  passing  off,  for  the  effect  is  the  same ;  so,  in  the  second 
case,  when  the  brush  of  light  appears,  we  may  consider  the 
positive  fluid  as  passing  off  from  the  point,  or  the  negative  fluid 
as  passing  on,  the  result  being  the  same. 

Electricity  cannot  be  long  preserved  on  a  body,  even  when 
well  insulated,  if  there  are  any  points  projecting  from  it,  as  the 
fluid  passes  freely  and  silently  from  points  into  the  air,  and  is 
lost.  Nor  can  the  fluid  be  retained  on  an  insulated  body  if 
there  are  points  of  other  inducting  bodies  near  turned  towards 
it.  The  fluid  will  escape  rapidly  to  these  points,  and  be  con- 
veyed away. 

549.  Though  we  have  spoken  of  glass  as  always  becoming 
positively  excited  by  friction,  and  sealing-wax  always  becoming 
negative,  yet  this  is  not  strictly  the  case.  It  is  found  that  when 
two  bodies  are  rubbed  together,  both  electricities  are  always 
excited  in  an  equal  degree,  one  of  them  passing  to  one  of  the 
substances  and  the  other  to  the  other.  This  may  be  proved 
experimentally  by  standing  on  a  stool  with  glass  legs,  called 
an  insulating  stool,  or  on  a  cake  of  beeswax,  when  the  glass 
tube  is  excited ;  the  tube  then  becomes  positive,  and  the  per- 
son and  rubber  negative.  To  show  that  the  person  himself 
becomes  negative  by  exciting  the  glass,  let  him,  while  standing 
on  the  insulating  stool,  present  his  hand  near  a  suspended  pith- 
ball,  previously  made  negative  by  touch- 
ing it  with  the  excited  sealing-wax.  As 
both  the  ball  and  the  hand  will  then  be 
negative,  the  ball  will,  of  course,  be  re- 
pelled. 

An  insulating  stand,  used  for  this  pur- 
pose, is  represented  in  figure  258 ;  it  con-  pjg.  258. 

conductor  is  presented  to  a  body  positively  excited,  what  is  the  appearance  ? 
What  if  held  near  a  body  negatively  excited  ?  Why  cannot  electricity  be 
retained  in  insulated  bodies  which  have  points  projecting  from  them  ?  What 
will  be  the  effect  of  points  directed  towards  an  excited  body  in  its  vicinity  ? 
549.  Will  glass  always  be  positively  excited  by  friction  ?  When  two  sub- 
stances are  rubbed  together,  are  both  electricities  always  excited?  How 
may  this  be  proved  experimentally  ?  What  will  be  the  electrical  state  of 
the  rubber  and  the  person  holding  it  ?  How  is  the  insulating  stand  formed  ? 


ELECTRICITY.  277 

sists  of  a  piece  of  strong  plank,  of  suitable  size,  with  strong 
glass  pillars  for  legs,  which  are  usually  coated  with  varnish. 

When  smooth  glass  is  rubbed  by  any  substance  except  cats' 
fur,  it  becomes  positive,  and  the  rubber  negative;  but  if  it  is 
rubbed  with  this  substance,  the  glass  becomes  negative  and 
the  fur  positive.  Sealing-wax  becomes  negative  when  rub- 
bed by  any  substance  except  a  piece  of  rough  glass  or  sul- 
phur, both  of  which  communicate  to  it  the  positive  electricity. 
When  paper  and  sealing-wax  are  rubbed  together,  the  paper 
becomes  positive  and  the  wax  negative;  but  when  paper  and 
smooth  glass  are  rubbed  together,  the  positive  fluid  goes  to  the 
glass  and  the  negative  to  the  paper. 

550.  The  Electrical  Machine.  —  By  rubbing  a  glass  tube  or 
a  stick  of  sealing-wax  a  number  of  times,  and  then  passing  it 
over  an  insulated  conducting  substance,  so  as  to  touch  it,  as  a 
ball  of  metal  supported  on  a  glass  pillar,  a  considerable  quan- 
tity of  electricity  may  be  collected ;  but  the  process  is  neces- 
sarily tedious.  To  accomplish  the  same  object  more  readily 
and  conveniently,  the  electrical  machine  has  been  invented ; 
the  essential  parts  of  which  are  a  glass  cylinder  or  plate,  capa- 
ble of  being  turned  by  the  hand;  a  rubber,  usually  made  of 
leather  or  silk,  and  placed  so  as  to  press  against  the  cylinder 
or  plate ;  and  a  prime  conductor,  to  receive  the  electricity  as  it 
is  generated.  It  is  made  of  metal,  and  supported  by  a  glass 
pillar. 

A  figure  representing  a  cylindrical  machine  will  be  found  in 
the  author's  Chemistry,  page  75.  Figure  259  represents  a  beau- 
tiful double  plate  machine,  belonging  to  the  Wesleyan  Uni- 
versity. It  was  made  by  Pixii,  of  Paris.  A  B  is  a  firm  base 
of  wood,  well  framed  together,  and  mounted  on  castors ;  P  P 
are  two  circular  glass  plates,  each  36  inches  in  diameter,  placed 
on  the  same  axis,  so  as  to  be  turned  at  the  same  time  by  the 
handle,  H ;  and  to  each  plate  are  four  rubbers,  R  R  R,  &c., 
placed  at  the  top  and  bottom  in  pairs,  one  at  each  place,  press- 
ing against  the  plate  on  each  side.  From  each  rubber  a  flap 
of  oiled  silk,  F,  extends  a  distance,  to  prevent  the  electricity 
from  being  dissipated  before  reaching  the  prime  conductor. 
C  C  C  C  is  the  prime  conductor,  made  of  sheet  brass,  and  sup- 
ported by  four  strong  glass  pillars;  it  receives  the  electricity 
from  the  plates  by  points  which  project  from  it  towards  them 
on  both  sides,  some  of  which  are  seen  in  the  figure. 

What  substance,  by  friction,  renders  glass  negative  ?  What  substances,  by 
friction  with  sealing-wax,  renders  it  positive  ?  What  is  said  of  the  effect 
produced  by  rubbing  together  paper  and  sealing-wax,  and  paper  and  glass  ? 
550.  How  may  an  insulated  conductor  be  electrified  by  means  of  a  glass  tube 
or  stick  of  sealing-wax?  What  is  the  design  of  the  electrical  machine? 
What  are  its  essential  parts  ?  What  is  the  use  of  the  glass  cylinder  or  plate  ? 
Of  the  rubber?  Of  the  prime  conductor?  What  is  the  rubber  made  of? 
How  is  the  electricity  received  upon  the  prime  conductor? 
24 


278 


NATURAL     PHILOSOPHY. 


MUMF.ORD    So. 


Fig.  259. 

551.  To  increase  the  effect  of  the  electrical  machine,  the  sur- 
face of  the  rubber  is  usually  spread  over  with  an  amalgam, 
made  by  melting  together  an  ounce  of  tin  and  3  ounces  of  zinc, 
and  then  pouring  in  two  or  three  ounces  of  mercury  previously 
heated.  When  cold  it  is  to  be  ground  to  a  fine  powder  in  a 
mortar,  and  mixed  with  a  sufficient  quantity  of  lard  or  tallow 
to  make  it  adhere  well  to  the  leather  or  silk  of  the  rubber. 

In  order  that  electricity  may  be  freely  developed  by  the  ma- 
chine, the  rubbers  must  not  be  insulated,  as,  in  this  case,  while 
the  prime  conductor  becomes  positively  electrified,  the  nega- 
tive fluid  accumulates  in  the  rubbers,  and,  after  a  few  turns 
of  the  plates,  little  further  effect  can  be  produced.  But  if  the 
rubbers  are  uninsulated,  the  negative  fluid  passes  off  freely  to 

Quest.  551.  What  is  the  use  of  the  amalgam  spread  upon  the  rubber? 
What  is  it  made  of?  Should  the  rubber  be  insulated  when  the  machine  is 
used? 


ELECTRICITY.  279 

the  earth,  while  a  constant  supply  of  the  positive  is  afforded 
for  the  prime  conductor. 

When  the  machine  is  to  be  used  it  should  be  placed  so  near 
a  fire  as  to  be  slightly  warmed,  and  every  part  made  perfectly 
dry.  It  should  also  be  made  perfectly  clean,  and  even  the  dust 
should  be  carefully  wiped  from  every  part. 

By  means  of  the  electrical  machine  the  preceding  experi- 
ments are  readily  performed,  as  well  as  others  to  be  hereafter 
described. 

552.  Various  Experiments.  —  When  electricity  is  passing 
freely  over  conducting  substances,  no  indications  of  it  are 
seen;  it  passes  silently  along,  and  mingles  with  that  in  the 
great  reservoir,  the  earth.  But  when  its  passage  is  interrupted 
by  a  non-conductor,  if  its  intensity  is  sufficient,  it  darts  across 
or  through  the  non-conductor,  presenting  the  appearance,  in 
the  dark,  of  a  bright  spark,  and  attended  with  a  smart  report, 
depending  upon  the  size  of  the  spark,  and  the  resistance  it  had 
to  overcome. 

The  spark  will  be  seen  by  presenting  the  knuckle  near  the 
prime  conductor  of  the  electrical  machine,  as  it  is  worked  ;  and 
at  the  same  time  a  slight  stinging  sensation  will  be  produced 
on  the  knuckle.  The" spark  will  be  seen  better  if,  instead  of 
the  knuckle,  a  metallic  ball,  on  the  end  of  a  piece  of  wire  held 
in  the  hand,  is  presented  to  the  conductor.  The  size  of  the 
spark,  and  the  distance  through  which  it  will  strike,  will  depend 
on  the  intensity  of  the  fluid  collected  in  the  prime  conductor, 
and  also  upon  the  diameter  of  the  ball  presented  to  it.  The 
colour  of  the  spark  will  vary,  being  sometimes  red,  then  purple, 
or  white  or  bluish.  It  seldom  passes  in  a  straight  line,  but 
makes  a  zigzag  course. 

The  human  body  is  a  good  conductor  of  electricity;  and  if 
a  person  places  himself  upon  an  insulating  stool,  and  holds  in 
his  hand  a  chain  connecting  with  the  prime  conductor,  as  the 
machine  is  turned  the  electricity  will  accumulate  in  every  part, 
so  that  a  spark  may  be  drawn  from  his  hands,  feet,  or  face,  in 
the  same  manner  as  from  the  prime  conductor. 

If  the  person  upon  the  insulating  stand  holds  a  metallic  spoon 
filled  with  ether,  in  his  hand,  and  another  standing  upon  the 
floor  presents  a  metallic  knob,  so  as  to  draw  a  spark  from  the 
liquid,  it  will  usually  be  inflamed. 

When  the  electric  spark  is  made  to  pass  through  a  chain, 
the  links  of  which  are  short,  in  a  dark  room,  it  appears  lumi- 

Quest.  552.  Are  any  signs  of  electricity  manifested  when  the  fluid  passes 
freely  over  good  conductors  ?  What  is  the  appearance  when  it  darts  over 
non-conductors?  How  may  the  spark  be  obtained  from  the  prime  con- 
ductor ?  What  is  the  sensation  produced  ?  What  is  said  of  the  colour  of 
the  spark  ?  How  may  the  spark,  be  received  from  the  face  or  hands  of  a 
person  ?  How  may  ether  be  inflamed  by  the  spark  ?  What  will  be  the 


280 


NATURAL     PHILOSOPHY. 


nous  through  its  whole  length  by  the  spark  passing  from  link 

to  link. 

Let  AB,  figure  260,  be  a  glass  tube,  an 
inch  in  diameter  and  2  feet  long,  having  a 
spiral  formed  on  it  from  end  to  end,  by  past- 
ing on  small  pieces  of  tin- foil,  so  as  to  be  at 
a  little  distance  from  each  other.  If,  while 
the  machine  is  turned,  one  end  of  this  is 
held  in  the  hand,  and  the  other  presented 
to  the  prime  conductor,  the  electric  spark 
will  dart  from  piece  to  piece  of  the  tin-foil, 
producing  a  train  of  light  over  the  spiral 
through  the  whole  length  of  the  tube.  The 
light  will,  of  course,  be  seen  best  in  a  dark 
room. 


Fig.  260. 


Let  a  plate  of  glass,  figure 
261,  have  a  very  narrow  strip 
of  tin-foil  pasted  on  it,  com- 
mencing at  A  and,  after  going 
several  times  backward  and 
forward,  terminating  at  B; 
then  let  several  letters  be 
formed  by  removing  portions  K 

of  the  tinfoil,  as  LIGHT,  and 

when  the  electric  spark  is  made  to  pass  over  the  foil  from  A  to 
B,  the  word  light  will  be  seen  written  in  letters  of  fire. 

553.  As  the  fluid  escapes  from  a  point  of  a  conducting  sub- 
stance, it  tends  to  produce  motion  in  the  point  in  the  opposite 
direction.  Let  A  BCD,  figure  262,  be  a 
cross  made  of  metal,  the  points  of  all  the 
wires  being  bent  at  right  angles  in  the 
same  direction ;  and  let  it  be  supported 
at  the  centre  upon  a  point  fixed  in  the 
prime  conductor,  E,  of  the  electrical  ma- 
chine. When  the  machine  is  worked,  the 
fluid  escaping  from  the  metallic  points 
will  cause  the  cross  to  revolve  rapidly  in 
the  direction  shown  by  the  arrows,  exhi- 
biting, in  the  dark,  a  complete  circle  of 
light,  as  it  escapes  from  the  points. 


Fig,  202. 


The  experiment  may  be  modified  in  the  following  manner, 
which  shows  the  mechanical  force  that  is  exerted.  Let  T, 
figure  263,  be  a  stand  of  wood,  with  four  pillars  of  glass  fixed 
in~it,  supporting  the  inclined  metallic  wires,  AB  and^CD;  and 
Jet  G  H I M  be  the  metallic  cross,  having  a  horizontal  axis,  E  F, 
also  of  metal,  resting  upon  the  inclined  wires.  Let  a  chain 


appearance  in  the  dark  if  the  spark  is  received  upon  a  tube  on  which  a  spiral 
of  pieces  of  tin-foil  has  been  formed  ?    553.  How  may  motion  be  produced 


ELECTRICITY 


281 


Fig.  263. 


now  connect  one  of  the  in- 
clined wires,  as  A,  with  the 
prime  conductor  of  the  ma- 
chine; and  as  it  is  turned, 
and  the  fluid  escapes  from 
the  points  of  the  cross,  as  be- 
fore, the  recoil  causes  it  to  re- 
volve around  the  axis,  EF, 
with  sufficient  force  to  roll  up 
the  inclined  plane. 

The  electrical  orrery  is  a 


very  beautiful  toy,  constructed  so  as  to  revolve  on  the  same 
principle,  by  the  escape  of  the  electric  fluid  from  points.  Let 
S,  figure  264,  represent  the  sun, 
E  the  earth,  and  M  the  moon, 
the  several  bodies  being  made 
of  such  a  weight,  respectively, 
that  S,  when  suspended  on  a 
wire,  W,  as  in  the  figure,  may 
just  balance  both  E  and  M,  and 
E  just  balance  M;  the  end  of 
the  wire,  W,  being  bent  up- 
wards, so  as  to  serve  for  a 
pivot  to  support  E  and  M.  The 
three  bodies,  thus  arranged, 
are  supported  on  an  insulating 
stand,  the  metallic  point,  A,  be- 
ing attached  to  a  cap  which 
is  cemented  upon  a  glass  pil- 
lar. A  metallic  chain  connects 
A  with  the  prime  conductor 
of  an  electrical  machine,  and  at  P  is  a  metallic  point,  and  also 
in  M,  from  which  the  electric  fluid  escapes,  causing  M  to  re- 
volve around  E,  and  both  M  and  E  to  revolve  around  S.  More 
properly,  S  and  the  othe*r  two  bodies,  considered  as  one,  revolve 
around  their  common  centre  of  gravity,  as  M  and  E  do,  also, 
around  their  centre  of  gravity ;  which,  in  fact,  is  what  really 
takes  place  among  the  bodies  of  the  solar  system  here  repre- 
sented. 

In  all  these  experiments,  in  which  motion  is  produced  by  the 
escape  of  electricity  from  a  point,  the  result  is  the  same,  whe- 
ther it  is  the  positive  or  the  negative  fluid  that  is  used. 

An  amusing  experiment  is  performed  by  cutting  several 
images  in  paper,  and  placing  them  between  two  metallic  plates, 
the  upper  one  of  which,  A,  figure  265,  is  suspended  by  a  chain 
from  the  prime  conductor  of  the  machine,  and  the  lower  one, 


Fig.  264. 


by  the  escape  of  electricity  from  a  point  ?    How  is  the  electrical  orrery 
constructed?    How  is  the  experiment  of  the  dancing  images  conducted? 
24* 


282 


NATURAL     PHILOSOPHY. 


Ill 

o    o    ^ 

A-  JC  B 


B,  connected  with  the  earth.  When  the  ma- 
chine is  turned  the  images  are  attracted  by 
the  upper  plate,  but  as  soon  as  they  come  in 
contact  with  it  they  are  repelled,  and  fall;  but 
striking  again  on  the  lower  plate,  their  electricity 
is  discharged,  and  they  are  again  attracted  to 
the  upper  plate,  as  before.  They  are  thus  made 
to  dance  in  the  most  lively  manner,  skipping 
from  side  to  side,  as  currents  of  air  may  happen 
to  move  them. 

Suspend  from  a  rod 
fixed  in  the  prime  con- 
ductor the  piece  of  appa- 
ratus  called  the  electric 
Fig.  265.  bells,  which  consists  of 
three  bells,  ABC,  figure  266,  attached 
to  a  metallic  rod;  the  first  two,  A  and 
B,  by  metallic  chains,  and  C  by  a  cord 
of  silk.  Between  the  bells  hang  two 
clappers,  by  silk  threads,  and  from  the 
central  bell,  C,  a  chain  extends  to  the 
table  or  floor.  On  turning  the  machine  Fig  ggg 

the  bells  A  and  B,  being  connected  with 

the  prime  conductor  by  conducting  substances,  will  become 
positively  electrified,  and  will  therefore  attract  the  clappers, 
which,  however,  after  contact  with  A  and  B,  are  immediately 
repelled  by  them,  and  attracted  by  the  central  bell,  C.  On 
coming  in  contact  with  this,  they  discharge  their  electricity, 
received  from  A  and  B,  and  are  again  attracted  by  them,  as 
before ;  and  thus  a  constant  ringing  is  produced,  as  long  as 
the  machine  is  turned.  At  every  motion  of  each  clapper,  it 
will  be  perceived,  a  portion  of  the  fluid  is  transferred  from  the 
outer  bells  to  the  central  one,  and  thence  to  the  earth,  the 
superabundant  electricity  of  the  prime  conductor 
being  thus  gradually  discharged. 

The  electric  spark  may  be  made  to  pass 
through  glass.  For  this  purpose  let  an  ounce 
vial,  A,  figure  267,  partly  filled  with  olive  oil,  be 
suspended  from  the  prime  conductor  of  the  ma- 
chine by  a  wire  passing  through  the  cork  and 
bent  so  that  the  end  may  press  against  the  glass 
on  the  inside,  as  shown  in  the  figure.  When  the 
machine  is  turned,  the  point  of  the  wire  becomes 
highly  electrified ;  and  by  presenting  near  it  a 
metallic  ball,  or  even  the  knuckle,  a  discharge 
Fig.  267.  will  take  place  through  the  side  of  the  vial,  a 


What  causes  the  bells  to  ring  in  the  piece  of  apparatus  illustrated  in  figure 
266  ?     How  may  the  electric  fluid  be  made  to  pass  through  glass  ? 


ELECTRICITY. 

very  small  perforation  being  made  just  at  the  point  of  the  wire. 
By  turning  the  vial  a  little,  and  making  a  line  of  perforations 
quite  around  it  by  successive  discharges,  it  may  at  length  be 
broken  in  two. 

554.  The  electric  fluid  or  fluids  reside  entirely  upon  the  sur- 
face of  bodies,  as  a  hollow  sphere  of  gold  is  capable  of  contain- 
ing just  as  much  electricity  as  if  it  were  solid.  Indeed,  it  seems 
to  be  retained  merely  by  the  pressure  of  the  atmosphere,  since, 
if  an  insulated  body  be  excited  and  placed  under  the  receiver 
of  the  air-pump,  it  loses  its  electricity  almost  instantly  when 
the  air  is  exhausted. 

_  555.  The  electric  spark  will  pass  much  farther  in 

rarefied  air  than  under  the  full  atmospheric  pres- 
sure. Let  A,  figure  268,  be  a  glass  receiver,  with  a 
metallic  cap  cemented  on  at  each  extremity.  Con- 
nected with  the  cap  C  is  a  stop-cock  and  screw, 
by  which  it  may  be  attached  to  the  air-pump;  and 
also  a  wire,  with  a  knob  at  the  extremity,  extend- 
ing a  distance  into  the  receiver.  Through  the 
other  cap,  B,  a  wire  passes,  air-tight,  with  a  knob 
at  each  extremity.  By  holding  this  in  the  hand, 
by  the  cap,  C,  near  the  prime  conductor,  it  will  be 
found  the  spark  will  pass  farther  when  the  air  has 
been  partly  exhausted  than  it  would  before  the 
exhaustion.  It  is,  of  course,  understood  that  the 
wire,  B,  is  made  to  slide  in  the  cap,  so  that  the 
balls  witm'n  tne  receiver  may  be  adjusted  to  differ- 
ent distances  from  each  other,  as  may  be  necessary. 
If  the  experiment  is  conducted  in  a  darkened  room,  when  the 
air  in  the  receiver  is  highly  rarefied,  and  the  ball  B  held  in 
contact  with  the  prime  conductor,  as  the  machine  is  turned,  a 
beautiful  stream  of  pale  light,  not  unlike  that  of  the  aurora 
borealis,  will  be  seen  between  the  balls  in  the  receiver.  If  a 
receiver  several  feet  long  is  used,  a  faint  nebulous  light  will  be 
seen  to  play  through  its  whole  length. 

556.  When  a  body  is  charged  with  electricity  it  may  be  dis- 
charged in  three  different  ways.  1.  The  fluid  may  be  con- 
veyed away  by  a  conducting  substance,  as  a  wire,  extending 
from  the  excited  body  to  the  ground.  This  is  called  the  con- 
ductive discharge.  2.  The  fluid  may  pass  by  a  spark,  as  when 
the  knuckle  is  held  near  an  excited  body,  or  when  the  spark 
is  made  to  pass  through  the  side  of  a  glass  vial  (§  553).  3.  The 
fluid  may  be  conveyed  away  from  an  excited  body  by  a  mo- 
tion communicated  to  the  particles  of  air  in  contact  with  the 

Quest.  554.  Do  the  fluids  in  excited  bodies  reside  entirely  upon  the  sur- 
face ?  555.  Will  the  spark  pass  farther  in  rarefied  air  than  under  the  full 
atmospheric  pressure  ?  What  is  said  of  the  appearance  of  the  electrical 
light,  as  the  fluid  passes  through  air  highly  rarefied  ?  556.  When  a  body  is 
charged  with  electricity,  in  what  three  ways  may  it  be  discharged  ?  Why 


284 


NATURAL     PHILOSOPHY. 


body.  This  always  takes  place  to  some  extent  when  a  body 
is  excited,  though  it  is  scarcely  perceived.  It  is  called  the 
convective  discharge.  It  is  by  this  discharge  that  the  fluid  col- 
lected in-a  body  will,  in  all  cases,  in  process  of  time,  be  con- 
veyed away. 

To  understand  why  the  particles  of  air  in  the  vicinity  of  the 
excited  body  should  be  put  in  motion,  it  is  necessary  only  to 
refer  to  what  takes  place  when  the  suspended  pith-ball  is 
brought  near  it  ($  537).  The  particles  of  air  are  first  attracted, 
and  then  repelled,  each  of  them  carrying  with  it  a  portion  of 
the  electricity  of  the  excited  body,  until  it  is  all  discharged. 

INDUCTION. 

557.  When  an  electrified  body  is  brought  near  another  which 
is  unelectrified,  the  natural  electricity  of  the  latter  is  disturbed 
by  the  influence  of  that  accumulated  in  the  former ;  and  the  term 
induction  is  used  to  indicate  the  general  phenomena  that  ensue. 

Let  A  B,  figure  269,  be  an 
==g  insulated  cylinder  of  metal, 
3  in  its  natural  state,  and  let 
S  be  a  sphere,  coated  with 
metal  and  supported  on  an 
insulating  pillar.  Then  let 
a  spark  of  positive  electri- 
city be  communicated  to 
the  sphere,  S;  it  will  in- 
stantly act  upon  the  natu- 
ral electricities  of  the  cylin- 
der, A  B,  which,  upon  exa- 
mination, will  be  found  to 
have  positive  electricity  at  the  extremity  B,  and  negative  elec- 
tricity at  the  other  extremity,  A,  while  near  the  centre,  between 
them,  it  will  be  neutral.  No  electricity,  it  is  supposed,  has 
passed  from  the  sphere  to  the  cylinder,  but  the  free  electricity 
of  the  sphere  has  exerted  an  influence  upon  the  natural  elec- 
tricity of  the  cylinder,  decomposing  it,  and  attracting  the  nega- 
tive to  the  end  A,  and  repelling  the  positive  to  the  end  B. 

558.  If  the  sphere,  S,  had  been  negatively  electrified,  the 
same  effect  would  have  been  produced  upon  the  electricity  of 
the  cylinder,  A  B,  except  that  the  end  A  would  have  become 
positive  and  the  end  B  negative.     Whether  the  sphere  were 
electrified  positively  or  negatively,  the  part  of  the  cylinder  far- 
thest from  it  would  have  the  same  kind  of  electricity,  and  the 
part  next  to  it  the  opposite  kind.    In  either  case,  too,  on  the 

are  the  particles  of  air  in  the  vicinity  of  an  excited  body  put  in  motion  ?  557. 
What  is  the  effect  when  an  electrified  body  is  brought  near  one  that  is  un- 
electrified ?  When  the  excited  sphere,  S,  figure  269,  is  brought  near  the 
insulated  cylinder,  AB,  what  effect  is  produced  upon  the  natural  electricity 
in  A  B  ?  558.  If  the  sphere,  S,  had  been  negatively  electrified,  what  would 


Fig.  269. 


ELECTRICITY.  285 

removal  of  the  excited  body,  the  natural  electricities  of  the 
cylinder  combine,  and  it  again  becomes  neutral  in  every  part. 
By  some  the  sphere,  S,  is  called  the  inductive,  and  the  cylin- 
der, A  B,  in  this  experiment,  the  inductric  body. 

559.  If  the  finger  be  presented  to  either  end  of  the  cylinder, 
AB,  while  under  the  influence  of  the  excited  sphere,  S,  a 
spark  will  be  received;   and  on  the  removal  of  the  sphere, 
AB  will  not  be  neutral,  as  before,  but  there  will  be  an  excess 
of  one  or  the  other,  according  as  the  finger  may  have  been 
presented  to  the  positive  or  negative  (§  558)  part  of  the  cy- 
linder. 

If  the  inductive  sphere  had  been  placed  near  the  centre  of 
the  cylinder,  then  both  extremities  would  have  the  same  elec- 
tricity as  the  sphere,  and  the  centre  the  opposite  kind.  In  any 
case  that  part,  or  those  parts,  of  the  inductric  (it  being  sup- 
posed to  be  insulated),  will  have  the  same  electricity  as  the 
inductive  body,  while  the  part  or  parts  near  it  will  have  the 
opposite  kind. 

560.  A  good  method  of  showing  the  inductive  influence  of  an 
electrified  body  upon  another  in  its  vicinity,  in  its  natural  state, 

is  as  follows : — Let  A  B,  figure 
270,  be  a  metallic  cylinder,  in- 
sulated upon  a  glass  pillar, 
bent  over  at  top  so  as  to  be 
attached  to  the  upper  side, 
and  let  pieces  of  pith-ball  be 
suspended  from  it  by  cotton 
threads  at  each  extremity  and 
at  the  centre.  While  the  cy- 
linder is  in  its  natural  state 
the  balls  will  hang  vertically, 
but  on  bringing  near  the  ex- 
cited sphere,  S,  the  balls  at 

each  extremity  will  diverge  with  free  electricity,  while  those 
in  the  centre  will  be  unaffected.  The  balls  at  B  diverge  with 
tne  same  kind  of  electricity  as  is  contained  in  the  sphere,  S, 
but  the  balls  at  A  with  the  opposite  kind. 

If  the  inductric  is  not  insulated,  and  is  of  limited  extent,  the 
whole  of  it,  while  under  the  influence  of  the  inductive,  will  take 
the  opposite  kind  of  electricity,  that  of  the  same  kind  naturally 
existing  in  it  being  driven  into  the  earth. 

have  been  the  result  ?  If  the  excited  body  is  removed,  what  will  be  the  ef- 
fect? 559.  If,  while  the  sphere,  S,  is  near  A  B,  the  finger  is  presented  to 
one  of  its  ends,  what  will  be  the  effect  ?  If  the  sphere  be  now  removed, 
will  the  cylinder  be  neutral  ?  If  the  sphere  is  placed  opposite  the  centre  of 
the  cylinder,  what  kind  of  electricity  would  the  ends  be  found  to  have  ? 
560.  If  the  cylinder  have  several  pairs  of  pith-balls  suspended  from  it  by  cot- 
ton threads,  as  in  figure  270,  how  will  those  suspended  from  different  parts 
be  affected  when  the  excited  sphere  is  brought  near  one  end  ?  If  the  induc- 
tric is  not  insulated,  and  is  of  limited  extent,  what  will  be  the  effect  of  the 
inductive  upon  it  ? 


286  NATURAL     PHILOSOPHY. 

561.  We  have  heretofore  seen  ($  544)  that  similarly  electrified 
bodies  repel  each  other,  while  bodies  dissimilarly  electrified 
attract.     This  principle  will,  no  doubt,  serve  to  explain  the 
phenomena  of  induction,  as  the  separation  of  the  electricities 
naturally  existing  in  a  body,  in  the  manner  we  have  seen, 
when  brought  near  another  excited  body,  seems  to  be  only  a 
natural  and  necessary  result  of  it. 

We  may  here  see  why  light  bodies  are  attracted  when 
brought  near  an  excited  body;  they  are  evidently  first  ren- 
dered electrical  by  the  inductive  influence  of  the  excited  body, 
and  then  attracted  by  virtue  of  their  being  in  the  opposite  elec- 
trical state.  Electrical  attraction  never  takes  place  between 
two  bodies  unless  they  are  in  opposite  states.  So,  when  the 
attracted  body  has  once  come  in  contact  with  the  excited  body, 
it  takes  a  portion  of  its  electricity,  and  is  then  repelled  as  having 
the  same  kind  of  electricity. 

562.  In  these  experiments  nothing  but  air  has  been  supposed 
to  intervene  between  the  excited  body  called  the  inductive,  and 
the  inductric,  or  body  acted  upon;  but  the  same  effect,  though 
in  different- degrees,  will  be  produced  through  glass,  wax,  sul- 
phur, or  other  non-conducting  substances ;  which,  when  thus 
used,  are  called  dielectrics. 

563.  The,  Electrophorus. —  The  electrophorus,  or  electricity 
bearer,  is  an  instrument  for  readily  obtaining  small  quantities 
of  electricity.     It  consists  of  a  circular  cake  of  resin,  contained 

in  a  shallow  tin  dish,  C  D,  figure  271,  and  a 
im  circular  metallic  disc,  AB,  a  little  smaller 

\  I  than  the  cake  of  resin,  furnished  with  an  in- 

j  sulating  handle  of  glass.     To  charge  it,  the 

metallic  disc  is  removed,  and  the  surface  of 
the  resin  rubbed  with  a  piece  of  dry  warm 
^^^^^  flannel,   by   which   it   becomes   negatively 
Fi<"  071  electrified,  and  is  capable  of  retaining  its 

electricity  for  a  great  length  of  time.  If  the 
metallic  disc,  A  B,  be  now  placed  upon  it,  by  means  of  its  insu- 
lating handle,  its  natural  electricity  will  be  decomposed  by  the 
inductive  influence  of  the  resin,  its  positive  electricity  being 
attracted  to  the  lower  surface,  while  the  negative  is  expelled 
to  the  upper  surface.  If  the  plate  of  metal  is  removed  by  its 
insulating  handle,  the  electricities  at  once  unite  as  before,  and 
no  indications  of  electricity  appear ;  but  if,  while  it  rests  upon 
the  cake  of  resin,  the  finger  is  touched  to  the  upper  surface,  a 

Quest.  561.  Why  are  light  bodies  attracted  when  brought  near  an  excited 
body  ?  Why  is  the  pith-ball  of  the  electrometer  repelled  after  contact  with 
an  electrified  body  ?  562.  Will  the  inductive  influence  of  an  excited  body 
be  exerted  through  other  non-conducting  substances  besides  air  ?  563.  What 
is  the  electrophorus  ?  What  does  it  consist  of?  How  is  it  charged  ?  When 
the  cake  of  resin  is  charged  by  friction,  what  is  the  effect  upon  the  natural 
electricity  of  the  metallic  plate  when  placed  upon  it  ?  If  the  finger  be  now 


ELECTRICITY.  287 

spark  of  negative  electricity  is  received  ;  and,  after  being  re- 
moved from  the  resin  by  its  insulating  handle,  it  will  be  elec- 
trified positively;  that  is,  an  excess  of  positive  electricity  will 
be  contained  in  it,  and  a  smart  spark  of  positive  electricity  may 
be  received  from  it. 

As  no  electricity  is  taken  from  the  cake  of  resin  in  this  expe- 
riment, if  the  disc  is  again  applied  to  it,  the  same  results  will 
follow  as  before  for  almost  any  number  of  times.  A  cake  of 
resin,  prepared  in  this  manner,  has  often  been  known  to  retain 
its  charge  for  weeks,  and  even  months,  though  not  without 
some  loss  of  intensity.  The  electrophorus  may  therefore  often 
be  used  as  a  substitute  for  the  electrical  machine,  when  only 
small  quantities  of  electricity  are  required. 

The  resin  cake  may  easily  be  prepared  by  melting  together  two  parts 
of  shel-lac  and  one  part  of  Venice  turpentine,  and  pouring  it,  while  warm, 
into  the  shallow  metallic  dish  prepared  for  it.  Care  should  be  taken  that 
the  surface  be  made  perfectly  smooth  and  even.  When  the  surface  of  the 
resin  is  negatively  excited,  the  metal  composing  the  dish  will  always  be 
positive. 

564.  An  amusing  and  not  uninstructive  experiment  may  be  performed 
with  the  cake  of  resin  thus  prepared,  as  follows : — Let  it  be  entirely  free 
from  electricity,  and  then  touch  it  in  several  places  with  some  positively 
electrified  body,  and  afterwards  in  several  other  places  with  another  body 
negatively  excited.     Then  grind  together  some  fine  red  lead  and  sulphur, 
and  introduce  the  mixture  into  a  common  hand-bellows,  and  blow  it 
against  the  face  of  the  cake  standing  on  its  edge.     The  two  substances 
will  entirely  separate  from  each  other,  one  adhering  to  those  points  which 
were  touched  by  the  positively  electrified  body,  while  the  other  will  attach 
itself  only  to  those  places  touched  by  the  negative  body.     The  reason,  no 
doubt,  is,  that  the  red  lead  and  the  sulphur,  by  friction,  become  excited, 
one  positively  and  the  other  negatively,  so  that,  when  blown  against  the 
cake  of  resin,  each  is  attracted  to  those  parts  of  its  surface  which  is  in 
the  slate  the  opposite  of  its  own. 

565.  Electrometers. — There  are  two  kinds  of  electrometers — 

those  which  are  used  simply  for  determining  the  pre- 
sence of  free  electricity,  and  those  which  are  used  for 
determining  both  its  presence  and  its  intensity.  Of 
the  first  kind  is  the  suspended  pith-ball,  figures  254 
and  255,  of  which  no  further  description  is  needed. 

The  gold-leaf  electrometer  is  a  more  sensitive  in- 
strument, and  may  be  used  to  indicate  the  presence 
of  smaller  quantities  of  electricity.  It  consists  of  a 
cylindrical  glass  vessel,  figure  272,  with  a  metallic 
bottom  and  a  metallic  cap  at  top,  from  which  two 
narrow  slips  of  gold-leaf  are  suspended  in  the  inside. 
Fig.  272.  When  an  electrified  body  is  brought  over  the  instru- 

presented  to  the  upper  surface  of  the  plate,  what  will  be  the  effect  ?  If  the 
plate  is  then  removed  by  its  insulating  handle,  what  will  be  its  electrical 
state  ?  May  this  process  be  often  repeated  ?  Will  the  resin  long  retain  its 
charge  ?  565.  What  two  kinds  of  electrometers  are  there  ?  How  is  the 
gold-leaf  electrometer  constructed?  How  does  it  show  the  presence  of 


288 


NATURAL     PHILOSOPHY. 


Fi    2?3 


ment,  the  gold  leaves  are  made  to  diverge  by  the  electricity 
induced  in  them  by  the  excited  body.  The  instrument  is  ex- 
ceedingly delicate. 

The  quadrant  electrometer,  figure  273,  con- 
sists of  a  graduated  semicircle  of  ivory,  A,  at- 
tached to  an  upright  support  of  wood,  D,  and 
a  light  index,  terminating  in  a  pith-ball,  C,  and 
moving  on  a  pin  fixed  in  the  centre  of  the  gra- 
duated semicircle.  When  this  instrument  is 
placed  on  any  electrified  body,  as  the  prime 
conductor  of  the  electrical  machine,  the  index 
is  made  to  rise  by  repulsion  ;  and  the  degree 
at  which  it  stands  is  supposed  to  indicate,  with 
some  accuracy,  the  comparative  intensity  of 
the  charge. 

566.  The  Ley  dan  Jar.—  This  piece  of  appa- 
ratus  has  received  its  name  from  the  city  of 
Leyden,  in  Holland,  where  it  was  invented. 
It  is  simply  a  glass  jar  or  phial,  figure  274,  of 
convenient  size,  coated  internally  and  externally 
with  tin-foil,  except  a  space,  some  three  inches 
Wide,  around  the  mouth.  For  conveniently  in- 
serting the  inside  coating,  a  vial  with  a  wide 
mouth  is  usually  selected.  Through  a  varnished 
wooden  cover,  A,  which  closes  the  mouth,  a 
brass  wire  passes,  having  a  ball  at  top,  and  at 
its  lower  end  a  chain,  B,  which  extends  to  the 
internal  coating. 

To  charge  the  jar  the  knob  at  top  is  to  be  held 
near  the  prime  conductor  of  the  machine,  when 
a  succession  of  sparks  will  be  seen  to  pass  be- 
tween it  and  the  prime  conductor.  The  positive 
electricity  then  collects  rapidly  on  the  inside 
coating,  and  by  its  inductive  influence  on  the  outside  coating, 
causes  an  equal  quantity  of  the  negative  to  collect  there,  at 
the  same  time  expelling  the  positive  naturally  contained  in  it  ; 
so  that,  when  the  jar  is  charged,  the  two  surfaces  are  in  oppo- 
site electrical  states. 

567.  When  charging  the  jar  the  outside  must  not  be  insu- 
lated, as  in  that  case  the  positive  fluid  which  is  naturally  con- 
tained in  it  could  not  escape,  and  then  the  outside  coating 
would  not  receive  the  positive  fluid  from  the  prime  conductor. 
A  series  of  jars  may  be  charged  at  the  same  time  by  con- 
necting the  external  coating  of  the  first  with  the  knob  of  the 

electricity?  How  is  the  quadrant  electrometer  constructed?  566.  From 
what  does  the  Leyden  jar  receive  its  name  ?  How  is  it  constructed  ?  How 
is  it  charged  ?  As  the  internal  surface  becomes  charged  with  positive  elec- 
tricity^ what  effect  is  produced  on  the  external  coating?  567.  Can  the  jar 
be  charged  while  the  external  coating  is  insulated  ?  What  is  the  reason  ? 
How  may  a  series  of  jars  be  charged  at  the  same  time  ? 


Fig.  274. 


ELECTRICITY. 


289 


second,  the  external  coating  of  the  second  with  the  knob  of  the 
third,  and  so  on,  all  except  the  last  being  supposed  to  be  insu- 
lated. Let  A  BCD, 
figure  275,  be  four 
Leyden  jars,  placed 
on  insulating  stools, 
and  connected  toge- 
ther as  shown  in  the 
figure,  the  knob  of 

Fi    275  the   first,   A,   being 

connected  with  the 

prime  conductor.  As  the  positive  fluid  accumulates  in  A,  it 
acts  by  induction  on  the  outside  coating,  separating  its  natural 
electricities,  and  causing  the  negative  to  accumulate  in  it,  while 
the  positive  passes  along  the  chain  to  the  inside  of  B.  In  B  the 
same  effects  are  then  produced  as  in  A,  and  so  on  to  the  end 
of  the  series,  the  outside  of  the  last  being  connected  with  the 
floor  of  the  room. 

568.  The  jar,  as  usually  charged,  contains,  as  we  have  seen, 
positive  electricity  in  the  internal  coating  and  negative  in  the 
external  coating :  but  it  may  be  charged  negatively ;  that  is,  so 
that  the  electricities  of  the  coatings  may  be  the  reverse  of  the 
above.    This  is  done  by  insulating  the  outside  of  the  jar,  and 
connecting  it  with  the  prime  conductor,  at  the  same  time  ex- 
tending a  wire  from  the  knob  to  the  table  on  which  the  appa- 
ratus is  placed. 

569.  The  Leyden  jar  is  discharged  by  forming  a  connection 
between  the  internal  and  external  coatings,  when  the  two  elec- 
tricities combine  with  a  loud  report.    By  making  the  commu- 
nication with  the  hands  the  fluids  pass  through  the  system, 
producing  the  electric  shock. 

To  prevent  the  passage  of  the 
charge  through  the  person  the  dis- 
charging-rod  is  generally  used. 
This  instrument,  figure  276,  is 
made  of  two  stout  wires,  connect- 
ed by  a  joint,  like  a  pair  of  com- 
passes, and  terminated  by  knobs, 
and  fixed  to  an  insulating  glass 
handle.  By  means  of  the  joint  it 
may  be  opened  to  different  dis- 
tances, as  may  be  required. 

Some  interesting  experiments  may  be  performed  by  means 
of  jars  having  the  coating  interrupted.    Diamond  jars,  figure 


Fig.  276. 


Quest.  568.  How  may  the  jar  be  charged  negatively  ?    569.  How  is  the 
jar  discharged  ?    How  is  the  electric  shock  produced  ?     What  is  the  use  of 
the  discharging -rod  ? 
25 


290 


NATURAL      PHILOSOPHY. 


277,  are  formed  by  pasting  small  pieces  of  tin-foil  at  short  dis- 
tances from  each  other,  both  outside  and  inside, 
except  the  bottom,  which  is  entirely  covered. 
Suppose,  now,  that  the  knob  is  connected  with 
the  prime  conductor ;  as  the  chain  extends  to  the 
bottom  of  the  jar,  the  coating  there  will  become 
charged  first,  and  the  fluid  will  extend  upward, 
on  the  inside,  from  piece  to  piece  of  the  coating, 
producing  beautiful  scintillations;  and,  at  th~e 
same  time,  a  similar  effect  will  be  produced  on 
the  outside,  as  the  pieces  of  coating  become 
charged  with  negative  electricity. 

570.  If  the  jar  is  provided  with  a  continuous 
metallic  coating  inside,  and  the  outside  coated 
Fig  277.  °y  covermg  it  with  solution  of  glue,  and  sprink- 
ling on  it  some  brass  filings,  when  it  is  connected 
with  the  prime  conductor,  as  the  positive  fluid  is  collecting  in 
the  internal  coating,  the  accumulation  of  the  negative  on  the 
outside  will  be  shown  by  the  darting  of  bright  sparks  over  it, 
very  much  resembling  flashes  of  lightning  that  are  often  seen 
in  the  clouds.  Around  both  the  top  and  the  bottom  there 
should  be  a  strip  of  tin-foil. 

Sometimes  two  or  more  Leyden  jars  are  used  together,  by 
connecting  all  the  interior  coatings  by  means  of  wires  extend- 
ing from  knob  to  knob,  and  all  their  exterior  coatings  by 
placing  them  in  a  box  lined  with  tin- 
foil. It  is  then  called  an  electrical  bat- 
tery, figure  278.  At  A  is  a  hook,  which 
connects  with  the  external  coatings  of 
the  jars.  The  effects  of  the  battery  are 
in  all  respects  the  same  as  would  be 
produced  by  a  single  jar  with  an  equal 
amount  of  surface ;  but  very  large  jars 
are  always  in  great  danger  of  being 
broken  by  the  recoil  produced  when 
they  are  discharged. 

571.  By  means  of  the  Leyden  jar  many  interesting  experi- 
ments may  be  performed,  illustrating  the  nature  of  this  subtle 
.element. 

To  pass  the  charge  through  any  body,  it  is  necessary  only  to 
cause  it  to  make  a  part  of  the  circuit  connecting  the  positive 
internal  coating  of  the  jar  with  the  negative  external  coating. 
The  piece  of  apparatus  called  the  universal  discharger  answers 
well  for  this  purpose ;  which  consists  of  two  stout  brass  wires, 

Quest.  570.  If  a  jar  is  coated  internally  with  tin-foil  and  externally  with 
metallic  filings,  what  will  be  the  appearance  as  it  is  charged  ?  What  is  the 
electrical  battery  ?  571.  How  may  the  charge  of  a  jar  be  passed  through  a 
body  ?  What  is  the  design  of  the  universal  discharger  ?  What  is  the  effeci 


Fig.  278. 


ELECT  RI C IT Y. 


291 


Fig.  279 


A  and  B,  figure  279,  supported  on 
glass  pillars,  C  and  D,  by  caps 
furnished  with  joints,  so  as  to  al- 
low them  to  turn  in  any  direc- 
tion. They  also  slide  in  the  caps, 
to  allow  the  balls  at  their  extre- 
mities to  be  placed  at  any  desired 
distance  from  each  other.  At  E 
is  a  table  of  wood,  which  may  be 
elevated  or  depressed  at  plea- 
sure, for  the  support  of  any  substance  to  be  submitted  to  ex- 
periment. 

Let  a  dry  card,  or  the  cover  of  a  book,  be  placed  between 
the  knobs  of  the  discharger,  and  the  charge  of  a  large  jar  be 
made  to  pass  through  it.  It  will  be  found  that  a  hole  is  pierced 
quite  through  it ;  and  it  will  be  burred  outward  on  both  sides, 
as  if  the  force  had  burst  outward  from  the  inside  of  the  card. 

Put  a  piece  of  gold-leaf  between  two  pieces  of  white  paper, 
press  them  lightly  together,  and  place  it  between  the  knobs  of 
the  discharger,  so  that  they  may  be  in  contact  with  its  oppo- 
site edges ;  after  the  discharge  the  paper  will  be  found  stained 
of  a  purple  colour  by  the  oxide  of  gold  which  has  been  formed. 
The  same  effect  will  be  produced  upon  pieces  of  glass  between 
which  a  piece  of  gold-leaf  has  been  placed,  and  made  to  convey 
the  electric  discharge ;  but  usually  the  glass  will  be  more  or 
less  broken. 

If  the  fluid  be  passed  through  a  piece  of  loaf  sugar,  or  of  fluor 
spar,  it  will,  for  a  moment,  shine  with  a  feeble  phosphorescent 
light. 

By  passing  the  charge  through  a  bunch  of  cotton  or  tow, 
over  which  some  powdered  rosin  has  been  sprinkled,  it  will 
often  be  inflamed. 

The  smallest  spark  of  electricity  is  capable  of  exploding  a 
mixture  of  oxygen  and  hydrogen  gases.  To  accomplish  this 
a  Leyden  jar  is  not  necessary,  a  mere  spark  from  the  prime 
conductor  being  sufficient.  The  spark,  of  course,  must  be  made 
to  pass  through  a  portion  of  the  mixture. 

Gunpowder  may  be  exploded -by  passing  through  it  the 
charge  of  a  Leyden  jar,  when  confined  in  a  small  space,  but 
not  without  some  difficulty.  The  experiment  succeeds  best 
when  a  piece  of  linen  or  cotton  thread,  well  soaked  in  water, 
makes  a  part  of  the  circuit. 

We  have  seen  above  (§  569)  the  mode  in  which  a  person  re- 
ceives the  electric  shock,  as  it  is  called ;  in  the  same  manner  a 
number  may  receive  it  at  the  same  instant,  by  grasping  each 

of  passing  the  charge  through  a  piece  of  dry  card  or  the  cover  of  a  book  ? 
How  may  a  strip  of  gold-leaf  be  oxydized  ?  What  will  be  the  effect  of  pass- 
ing a  charge  through  a  piece  of  loaf  sugar  or  fluor  spar  ?  What  other  expe- 
riments are  described  ?  How  may  gunpowder  be  fired  ? 


292  NATURAL     PHILOSOPHY. 

other's  hands  and  forming  a  line,  the  person  at  one  end  of  the 
line  pressing  his  hand  against  the  outside  of  the  charged  jar, 
and  the  one  at  the  other  end  presenting  his  knuckle  to  the  knob. 

572.  It  was  long  supposed  that  the  passage  of  electricity  over 
conductors  is  instantaneous,  but  it  is  now  found  such  is  not  the 
fact.    By  some  very  beautiful  experiments  it  has  been  shown 
that  the  fluid  passes  over  copper  wire,  and  probably  other  con- 
ducting bodies,  at  the  rate  of  about  288,000  miles  a  second, 
which  is  considerably  more  rapid  than  light  (§  337). 

573.  The  Condenser. — This  is  a  piece  of  apparatus  for  collecting  toge- 
ther or  condensing  in  a  small  space,  so  as  to  render  its  action  perceptible, 

very  feeble  electricities.  It  consists  of  two  metallic 
A  discs,  A  and  B,  figure  280,  placed  face  to  face,  and 

\  \(  separated  only  by  a  coating  of  resinous  varnish, 

with  which  they  are  covered.  The  upper  plate,  A, 
A  II D  called  the  collecting  plate,  has  attached  to  its  centre 


g  Q  a  glass  handle,  C,  by  which  it  may  be  lifted  from 
"^  \r';B  the  condensing  plate,  B,  and  from  its  edge  a  wire 

f  ^\  projects,  terminated  by  a  metallic  knob,  D.  By 

this  it  may  be  put  in  connection  with  another  body, 
the  electrical  state  of  which  it  is  proposed  to  exa- 
mine. The  condensing  plate,  B,  is  supported  by  a  metallic  stand,  and,  of 
course,  is  uninsulated. 

If  we  now  connect  any  feebly  electrified  body  with  the  knob,  D,  a  por- 
tion of  its  electricity  will  be  diffused  over  the  whole  plate  A,  and,  by  its 
inductive  influence,  the  opposite  kind  will  be  collected  in  B  (§  557) ;  this, 
in  turn,  will  react  upon  A,  and  thus  draw  into  it,  or  condense  in  it,  a 
larger  quantity  of  the  fluid  than  it  would  otherwise  have  possessed.  By 
separating  A  first  from  the  feebly  electrified  body,  and  then  raising  it 
carefully  by  its  glass  handle  from  the  plate  B,  the  electricity  it  contains 
may  be  examined  at  leisure.  Often  a  considerable  quantity  may  thus  be 
collected  in  the  plate  from  a  body  so  feebly  electrified  as  to  be  scarcely 
capable  of  affecting  the  nicest  electrometer. 

I£  while  the  plates  are  in  the  position  indicated  in  the  figure,  the  disc, 
A,  should  be  examined  by  the  electrometer,  it  would  scarcely  give  any 
signs  of  electric  excitement,  since  most  of  the  fluid  contained  in  it  would 
be  held  there  by  the  opposite  electricity  of  the  lower  plate.  This  electri- 
city thus  concealed  in  A  is  called  dissimulated  or  latent  electricity,  in 
opposition  to  free  electricity,  which  alone  is  capable  of  acting  on  the  elec- 
trometer. 

574.  The  Hydro-Electric  Machine. — It  has  recently  been  discovered  that 
electricity  is  rapidly  evolved  by  a  jet  of  steam  as  it  escapes  from  a  common 
steam-boiler ;  and  it  has  been  determined  that  it  is  occasioned  by  the  fric- 
tion of  the  steam  and  particles  of  condensed  water  against  the  sides  of 
the  pipe.  The  hydro-electric  machine,  therefore,  consists  of  a  strong 
steam-boiler,  which  is  to  be  insulated,  having  many  small  pipes,  through 
all  of  which  the  steam  may  be  allowed  to  escape  at  the  same  time.  As 
the  steam  escapes  the  boiler  becomes  highly  charged  with  electricity,  in 
some  cases  throwing  off  sparks  to  the  distance  of  two  feet,  or  more. 

Quest.  572.  What  is  the  velocity  with  which  the  electric  fluid  passes  over 
copper  wire  ?  573.  What  is  the  design  of  the  condenser  ?  What  does  it 
consist  of?  574.  What  occasions  the  electricity  developed  by  a  jet  of  steam  ? 


ELECTRICITY.  293 

ATMOSPHERIC    ELECTRICITY. 

575.  The  atmosphere,  especially  when  in  a  dry  state,  is,  as 
we  have  before  seen  (§  546),  a  non-conductor,  consequently  it 
is  capable  of  retaining  either  of  the  electric  fluids  communicated 
to  it;  and  different  portions  of  it,  or  different  strata,  may  be  in 
different  electrical  states  at  the  same  time.     This,  we  know  by 
experiment,  is  often  the  case.    Usually,  in  fair  weather,  the  air 
near  the  surface  is  positive,  and  the  intensity  increases  as  we 
ascend,  while  the  surface  of  the  earth  beneath  is  negative.    In 
stormy  weather,  at  all  seasons  of  the  year,  the  air  near  the  sur- 
face is  sometimes  positive  and  sometimes  negative ;  and  not 
unfrequently  sudden  changes  take  place  from  one  state  to  the 
other. 

576.  The  usual  method  of  determining  the  electrical  state  of 
the  air,  or  that  portion  of  it  near  the  earth,  is  to  erect  a  pointed 
metallic  rod  some  30  feet  in  length,  and  insulate  it,  connecting 
its  lower  extremity  only  with  the  electrometer,  or  such  other 
electrical  apparatus  as  it  may  be  necessary  to  use.    If  the  elec- 
tric bells  are  connected  with  the  rod,  the  presence  of  electricity 
of  sufficient  intensity  will  always  be  indicated  by  their  ringing, 
but  they  will  not  be  affected  when  the  electricity  is  very  feeble. 

577.  It  has  not  yet  been  satisfactorily  determined  by  what 
means  the  electricity  of  the  atmosphere  is  developed.   Various 
causes  have  been  assigned,  as  the  evaporation  that  is  constantly 
taking  place  at  the  surface,  and  the  condensation  of  vapours  in 
the  upper  regions  of  the  atmosphere;  but  recent  investigations 
render  it  probable  that  it  is  occasioned  by  the  friction  of  cur- 
rents of  air  against  each  other,  and  against  the  earth,  and  also 
against  particles  of  water  and  other  substances  which  are  al- 
ways floating  in  it.     Consequently,  vivid  lightnings  usually 
attend  the  eruptions  of  volcanoes,  especially  in  those  cases  in 
which  immense  columns  of  black  smoke,  composed  of  dust  and 
ashes,  are  belched  forth  into  the  air.   The  lightning  is  also  often 
attended  by  thunder. 

578.  The  clouds,  which  are  only  masses  of  aqueous  vapour 
partially  condensed  by  the  cold  of  the  upper  strata  of  the  at- 
mosphere, being  tolerably  good  conductors,  serve  to  collect  the 
free  electricity  of  the  atmosphere,  and,  therefore,  often  become 
highly  excited,  and  discharge  their  electricity  from  one  to  ano- 
ther, or  to  the  earth,  producing  all  the  phenomena  of  thunder 

Quest.  575.  Is  atmospheric  air  a  non-conductor  ?  May  different  strata  of 
it  be  in  opposite  electrical  states  ?  In  fair  weather  what  is  usually  the  state 
of  the  air  near  the  surface  ?  Does  the  intensity  increase  upward  ?  What  is 
the  state  of  the  surface  of  the  earth  beneath  ?  In  stormy  weather  what  is 
the  state  of  the  air  ?  576.  What  is  the  usual  mode  of  determining  the  elec- 
trical state  of  the  atmosphere  ?  577.  What  probably  occasions  the  electri- 
city of  the  atmosphere  ?  Are  lightnings  generally  seen  to  attend  volcanic 
eruptions,  when  immense  volumes  of  dust  and  ashes  are  belched  forth  into 
the  air?  578.  What  are  clouds?  May  they  become  highly  excited,  an4 
25* 


294  NATURAL     PHILOSOPHY. 

and  lightning.  Franklin  was  the  first  to  suggest  this  explanation 
of  lightning  and  thunder,  about  a  century  ago,  and  soon  after- 
wards proved  the  truth  of  his  suggestion  by  actual  experiment. 
This  he  did  by  sending  up  a  large  kite,  held  by  a  hemp  string, 
which  conducted  the  fluid  freely  downward,  especially  as  soon 
as  it  was  moistened  a  little  by  the  falling  rain.  At  the  lower 
end  a  short  piece  of  silk  cord  was  used,  in  order  to  insulate  it. 
With  this  apparatus  he  obtained  sparks,  charged  the  Leyden 
jar,  and  performed  other  electrical  experiments,  which,  since 
his  day,  have  often  been  repeated. 

579.  A  thunder-cloud  is  to  be  considered  the  same  as  any 
other  cloud,  except  that  it  is  charged  with  electricity.     Such 
clouds,  in  New  England,  usually  make  their  appearance  in  the 
west  or  north-west,  in  the  afternoon  or  evening,  during  the 
warm  weather  of  summer,  and  gradually  approach,  all  the  time 
increasing  in  size  and  blackness,  until  at  length  they  pass  over 
our  heads  and  disappear  in  the  east  or  south.   During  the  whole 
time  frequent  lightnings  and  thunder  are  taking  place,  with  the 
fall  of  more  or  less  rain,  and  sometimes  hail.    Not  unfrequently 
damage  is  done  and  Jives  are  lost  by  the  lightning  striking 
buildings,  trees,  and  other  elevated  objects. 

The  discharge  from  such  a  cloud,  which  we  call  lightning, 
differs  in  nothing,  it  is  believed,  from  the  discharge  of  a  spark 
from  the  prime  conductor  of  an  electrical  machine,  when  the 
knuckle  is  presented  to  it,  except  in  the  quantity  and  intensity 
of  the  fluid. 

580.  Let  us  suppose  a  cloud  positively  electrified  to  be  pass- 
ing over  a  place,  the  earth  and  everything  upon  its  surface  be- 
neath it  for  a  distance  will  become  negative  by  induction  (§  557), 
and  whenever  the  cloud,  in  its  passage,  comes  sufficiently  near 
the  earth,  or  any  object  upon  its  surface,  a  discharge  will  ensue 
between  the  earth  and  cloud.    The  distance  at  which  the  dis- 
charge will  take  place  will  depend  upon  circumstances,  as  the 
extent  of  the  surface  of  the  cloud  electrified,  its  intensity,  the 
conducting  power  of  the  air  and  vapours  contained  in  it  at  the 
time,  &c.     Circumstances  will  also  determine  the  direction  the 
fluid  will  take,  or  the  object  upon  the  surface  that  will  be  struck. 
Other  things  being  equal,  the  fluid  always  takes  the  course 
where  the  best  conductors  are  situated,  but  sometimes  it  will 
take  a  course  through  a  series  of  poorer  conductors,  provided 
the  distance  is  less  than  through  the  good  conductors. 

discharge  their  electricity  to  the  earth  ?  Who  first  suggested  this  explana- 
tion of  thunder  and  lightning  ?  How  did  he  prove  the  truth  of  the  sugges- 
tion ?  579.  From  what  part  of  the  heavens  do  thunder-clouds  usually  ap- 
pear to  rise  in  New  England?  Does  the  discharge  from  a  thunder-cloud 
differ  essentially  from  the  discharge  of  the  spark  from  the  prime  conductor 
of  an  electrical  machine  ?  580.  When  a  cloud  positively  electrified  is  pass 


ing  over  a  place,  what  will  be  the  electrical  state  of  the  surface  of  the  earth 
and  other  objects  beneat1  ' 
will  the  distance  depend 


and  other  objects  beneath  it  ?    When  will  a  discharge  take  place  ?    What 
1  upon  at  which  this  will  take  place  ?   What  will  de 


ELECTRICITY.  295 

Lightning,  it  is  well  known,  almost  always  strikes  the  high- 
est objects  at  their  highest  point,  though  there  are  occasionally 
exceptions;  and  in  its  course  it  often  rends  in  pieces  the  firm- 
est substances,  occasionally  setting  them  on  fire.  Sometimes 
its  course  can  be  traced  a  distance  in  the  earth,  after  leaving 
the  object  it  first  struck,  but  it  is  generally  soon  diffused  abroad, 
and  its  mechanical  effects  cease.  All  these  effects  are  just  such 
as  we  might  expect  to  be  produced  by  an  immense  electrical 
machine,  provided  we  were  able  to  construct  one  of  sufficient 
power. 

581.  When  a  spark  is  received  from  the  prime  conductor  of 
the  machine,  or  when  the  Leyden  jar  is  discharged,  a  single 
report  only  is  heard ;  whereas  thunder,  which  is  merely  the  re- 
port of  the  electric  discharge  from  the  clouds,  is  often  a  long- 
continued-rolling  sound.  This,  it  is  believed,  is  occasioned  by 
numerous  echoes  from  the  masses  of  cloud  scattered  at  various 
distances  from  the  ear  of  the  observer,  which,  of  course,  will 
arrive  successively  to  the  ear,  and  occasion  an  apparent  repe- 
tition (§  303)  of  the  original  report.  It  may  be,  indeed,  as  has 
been  suggested,  that  the  sound  itself  is  not  produced  at  a  single 
point,  but  along  the  whole  line  constituting  the  pathway  of  the 
fluid ;  and  the  original  report  may  then  be  considered  as  a  suc- 
cession of  reports  originating  at  different  distances  from  the 
ear,  and  though  produced  all  along  the  line  at  the  same  instant, 

B  yet  necessarily  arriving 
successively.  Thus,  let 
A,  1,2,  3,  B,  figure  281, 
be  the  path  of  the  fluid 
at  an  explosion  or  dis- 
charge, and  let  O  be  the 
place  of  the  observer ; 
if  the  sound  is  supposed 
to  be  produced  all  along 
this  line,  it  is  plain  that 
the  sound  from  the 

nearest  point,  as  1,  would  arrive  at  O  first,  then  that  from  other 
points  in  succession,  according  to  their  distance.  The  effect 
would  evidently  be  the  same  as  we  witness  in  the  continued 
rolling  sound  of  thunder.  And  the  path  of  the  fluid  is  not 
straight,  but  zigzag,  backward  and  forward,  as  represented  in 
figure  282,  which  we  may  suppose  greatly  to  increase  this 
peculiarity. 

termine  the  direction  the  fluid  will  take  ?  What  parts  of  objects  does  light- 
ning usually  strike  ?  581.  What  is  believed  to  occasion  the  continued  roll- 
ing sound  of  thunder  ?  May  the  sound  be  supposed  to  be  produced  at  dif- 
ferent points  along  the  path  of  the  fluid  ?  How  would  this  occasion  it  to 
appear  protracted  to  the  ear  ? 


296 


NATURAL     PHILOSOPHY, 


Fig.  282. 

582.  As  lightning  usually  strikes  the  highest  objects,  and  fol- 
lows the  course  of  the  best  conductors,  it  is  not  difficult  to  de- 
termine the  position  of  the  greatest  safety.     If  the  person  is  in 
a  building,  he  should  remove  as  far  as  possible  from  the  chimney, 
the  soot  of  which  often  serves  as  a  very  good  conductor  to  the 
fluid,  and  from  any  large  timbers  the  house  contains,  especially 
those  leading  downward  from  any  part  of  the  roof;  he  should 
also  remove  to  a  distance  from  any  metallic  conductor  passing 
through  the  house,  as  a  stove-pipe,  or  bell- wire,  or  pipe  for  con- 
veying water,  as  all  these  might  convey  the  fluid  directly  to  him. 
Probably  no  place  is  more  secure  than  a  seat  a  little  elevated  in 
the  centre  of  a  room.    It  is  well  ascertained  that  pieces  of  metal 
of  any  kind  carried  about  the  person  increase  the  danger. 

In  the  open  air  no  place  is  more  secure  than  an  open  field ; 
and  a  person  lying  horizontally  would  be  less  likely  to  be 
struck  than  if  he  were  standing  erect.  But  the  danger  will  be 
greatly  increased  by  carrying  an  umbrella,  or  by  seeking,  as 
is  often  done,  the  shelter  of  a  tree. 

583.  The  distance  of  an  electrified  cloud  may  be  estimated 
by  noticing  the  number  of  seconds  that  elapse  after  the  light- 
ning is  seen  before  the  thunder  is  heard.    As  sound  moves 
about  1125  feet  (§  300),  or  nearly  a  fifth  of  a  mile,  in  a  second, 
while  the  passage  of  light  for  so  small  a  distance  may  be  con- 
sidered Instantaneous,  it  is  evident  the  explosion  must  take 
place  at  the  distance  of  about  a  mile  for  every  five  seconds  of 
time  that  thus  elapse. 

Quest.  582.  Where,  within  a  building,  is  the  position  of  greatest  safety 
during  a  thunder-storm  ?  Will  pieces  of  metal  worn  about  the  person  in- 
crease the  danger  ?  What  position  is  considered  most  secure  for  a  person 
in  the  open  air  ?  What  is  said  of  the  propriety  of  seeking  shelter  under  a 
tree  ?  How  may  the  distance  of  an  electrified  cloud  be  estimated  ?  583. 
How  far  will  the  cloud  be  for  every  five  seconds  that  elapse  after  the  light- 
ning is  seen  before  the  thunder  is  heard  ? 


ELECTRICITY.  297 

584.  Lightning-rods,  or,  as  the  French  call  them,  paraton- 
nerres,  are-  metallic  rods,  attached  to  buildings  and  other  ob- 
jects, and  extending  a  distance  above  them,  to  protect  them 
from  danger  from  electric  discharges  between  the  clouds  and 
the  earth.    They  are  usually  made  of  iron,  and  should  always 
extend  several  feet  above  the  highest  point  of  the  object  to  be 
protected,  and  terminate  in  a  point ;  and  should  also  connect 
at  the  bottom  with  the  moist  earth.    The  rod  should  not  be 
less  than  half  an  inch  in  diameter,  and  it  is  of  little  consequence 
whether  it  be  round  or  square.    It  should  also  be  made  of  as 
few  pieces  as  possible,  and  these  should  be  brought  firmly  in 
contact,  as  by  screwing  one  into  the  other.    If  a  large  building 
is  to  be  protected,  there  will  be  an  advantage  in  using  several 
smaller  rods  instead  of  one  large  one ;  but  they  should  all  be 
connected  together,  and  should  have  branches  extending  to  all 
the  more  exposed  parts  of  the  building. 

585.  The  benefit  of  electrical  conductors  to  buildings  and 
other  objects  liable  to  injury  by  being  struck  by  lightning  is 
twofold.    In  the  first  place,  if  a  discharge  actually  takes  place 
upon  the  building,  the  conductor,  if  properly  constructed,  will 
almost  certainly  convey  the  fluid  harmless  to  the  ground.    Oc- 
currences like  this  have  been  frequent.    And,  when  buildings 
unprovided  with  proper  electrical  conductors,  but  having  me- 
tallic wires  or  bars  extending  through  them,  have  been  struck, 
it  has  generally  been  found  that  the  fluid  has  followed  the  metal 
as  far  as  it  extended  on  its  course,  and  has  damaged  the  build- 
ing only  before  reaching  the  metal,  or  after  leaving  it.  It  there- 
fore not  unfrequently  happens,  that  buildings  having  metallic 
tubes  for  conveying  the  water  from  the  eaves  downward,  when 
struck  by  lightning,  are  injured  only  in  the  roof,  the  fluid  from 
this  point  following  the  tube  to  the  ground. 

In  the  second  place,  electrical  conductors  attached  to  build- 
ings, when  properly  connected  with  the  moist  earth,  seem  to 
convey  the  electricity  of  the  clouds  silently  to  the  earth,  and 
thus  often,  no  doubt,  prevent  a  disruptive  discharge,  which 
might  otherwise  have  occurred,  and  done  great  injury.  The 
effect  of  presenting  a  pointed  conductor  in  the  vicinity  of  an 
electrified  body  we  have  heretofore  (§  548)  seen.  If  a  person 
standing  near  the  prime  conductor  of  an  electrical  machine 
presents  in  its  vicinity  the  point  of  his  pen-knife,  as  the  ma- 

Quest.  584.  What  is  the  design  of  the  lightning-rod  ?  How  is  the  light- 
ning-rod made  ?  How  should  it  terminate  at  the  top  ?  With  what  should 
it  connect  at  the  bottom  ?  Will  there  be  an  advantage  in  having  several 
rods  connected  together  for  a  large  building  ?  585.  In  case  a  discharge  actu- 
ally takes  place  upon  a  building,  how  does  the  conductor  protect  it  ?  Why 
are  buildings  provided  with  water-conductors,  extending  from  the  eaves 
downward,  often  injured  only  in  the  roof?  Do  lightning-conductors,  in  all 
probability,  often  convey  the  electricity  of  the  clouds  silently  to  the  earth, 
and  thus  prevent  a  disruptive  discharge  ?  What  will  be  the  effect  if  a  per- 
eon  standing  near  an  electrical  machine,  as  it  is  turned,  presents  the  point 


298  NATURAL     PHILOSOPHY. 

chine  is  turned,  scarcely  any  electricity  will  be  collected,  as  it 
will  nearly  all  be  conveyed  away  by  the  metallic  point.  And 
the  same  effect  will  be  produced  upon  the  electricity  of  the 
clouds  by  pointed  conductors  presented  towards  them. 

586.  When  the  atmosphere  is  highly  charged  with  electricity 
the  points  of  bodies  projecting  into  the  air  often  appear  lumi- 
nous in  the  dark.    This  was  probably  the  cause  of  the  fire  seen 
upon  the  points  of  the  spears  of  a  division  of  the  Roman  army, 
in  ancient  times,  mentioned  in  history  ;  and  it  is  here,  too,  we 
are  to  look  for  an  explanation  of  meteors  often  seen,  during 
storms,  upon  the  extremities  of  the  masts  and  spars  of  ship- 
ping, called,  by  sailors,  Castor  and  Pollux,  or  fire  of  St.  Elmo. 
The  points  of  electrical  conductors  attached  to  buildings  have 
been  known  to  present  the  same  appearance  when  highly  elec- 
trified clouds  have  been  passing  over  them ;  and  there  can  be 
no  doubt  the  cause  in  each  case  is  the  same. 

587.  That  conductors  attached  to  buildings  do  really  protect 
them  from  injury  from  lightning  has  been  abundantly  proved 
by  actual  experiment  a  thousand  times.     It  is  a  remarkable 
fact,  as  Arago  suggests,  that  the  temple  at  Jerusalem,  which 
stood  from  the  time  of  Solomon  until  the  year  70  of  the  Chris- 
tian era,  a  period  of  about  1000  years,  though  situated  on  an 
eminence  in  a  region  where  thunder-storms  are  common,  we 
have  reason  to  believe  from  the  silence  of  history,  was  never 
once  struck  by  lightning.     The  reason  plainly  was,  that  it  was 
protected  by  its  thick  gilding,  it  having  been  entirely  overlaid 
with  gold  ;  and  each  end  of  the  roof  was  adorned  with  a  row 
of  long  lances  of  iron,  which  were  pointed  at  top,  and  gilt. 
Metallic  pipes,  for  water-conductors,  also,  extended  from  the 
roof  to  cisterns  constructed  under  the  porch.    The  building 
was,  therefore,  admirably  protected  from  danger  from  light- 
ning, in  close  accordance  with  the  most  approved  principles 
of  modern  science. 

588.  Water-Spouts  and  Land-Spouts. — Water-spouts,  which 
are  often  seen  at  sea,  apparently  consist  of  dense  columns  of 
aqueous  vapour,  extending  from  the  clouds  to  the  surface  of 
the  ocean.     They  are  usually  observed  to  form  as  follows : — 
A  dense  black  cloud,  floating  in  the  air,  is  seen  to  have  form- 
ing on  its  under  side  an  inverted  cone,  which  rapidly  increases, 
extending  itself  downward;  and  the  surface  of  the  water  be- 
neath, which  before  had  been  tranquil,  begins  to  be  agitated, 
and  apparently  to  boil ;  and  soon  an  immense  column  rises, 
with  a  rapid  whirling  motion,  until  it  joins  the  inverted  cone 

of  his  pen-knife  in  the  vicinity  of  the  prime  conductor  ?  586.  What  is  said 
of  the  appearance  in  the  dark  of  the  points  of  objects  projecting  in  the  air 
when  highly  electrified  ?  Are  meteors  often  seen  by  sailors,  during  storms, 
upon  the  ends  of  the  masts  and  spars  of  ships  ?  587.  What  reason  is  given 
why  the  temple  of  Solomon,  at  Jerusalem,  was,  as  we  believe,  never  struck 
by  lightning?  588.  What  do  water-spouts  apparently  consist  of?  What  is 


ELECTRICITY.  299 

connected  with  the  cloud,  thus  forming  a  whirling  pillar  of 
dense  vapour,  reaching  from  the  cioud  to  the  surface  of  the 
sea.  Not  unfrequently,  two  or  more  of  these  are  seen  in  the 
immediate  vicinity  of  each  other,  as  represented  in  figure  283. 


Fig.  283. 

The  cause  of  the  formation  of  water-spouts,  no  doubt,  is  the 
highly  electrified  state,  either  positive  or  negative,  of  the  clouds, 
inducing  the  opposite  state  in  a  portion  of  the  sea  below  them. 
By  the  attraction  of  the  opposite  electricities  they  are  then 
drawn  together,  the  water  of  the  sea  rising  in  the  form  of  spray 
or  vapour,  while  a  portion  of  the  cloud  descends,  until  the  two 
unite  and  a  communication  is  established  between  them.  Dur- 
ing the  continuance  of  the  phenomena,  therefore,  which  some- 
times is  only  a  few  minutes,  and  at  others  several  hours,  often 
no  lightning  or  thunder  is  observed,  as  the  opposite  electrici- 
ties are  silently  discharged  through  the  continuous  conducting 
medium  which  is  in  this  extraordinary  manner  established. 
At  other  times  they  are  attended  by  violent  thunder  and  light- 
ning, or  merely  by  flashes  of  light  without  a  report.  The  whirl- 
ing motion  is  probably  produced  by  the  rushing  of  the  sur- 
rounding air  and  vapours  towards  the  centre  of  the  influence, 
where  the  column  is  formed. 

589.  Ships  coming  in  contact  with  water-spouts  have  oflen 
been  inundated  with  torrents  of  water,  and  destroyed ;  but,  in 

the  mode  in  which  they  have  been  observed  to  form  ?  What  is  the  cause  of 
their  formation  ?  Are  they  often  attended  by  lightning  and  thunder  ?  How 
is  their  whirling  motion  accounted  for  ?  589.  Are  ships  in  danger  of  being 
destroyed  in  coming  in  contact  with  them  ? 


300  NATURAL     PHILOSOPHY. 

some  instances  they  have  escaped.  When  they  are  seen  near 
a  ship  of  war,  the  sailors  often  attempt  to  fire  a  cannon-shot 
into  them,  by  which,  it  is  said,  they  may  often  be  broken  and 
destroyed,  and  the  danger  from  them  avoided. 

590.  Land-spouts  appear  to  be  produced  in  the  same  manner 
as  water-spouts,  except  that  they  occur  over  the  land  instead 
of  the  sea.    They  are  usually  attended  by  a  violent  whirlwind, 
which  levels  everything  in  its  course,  destroys  buildings,  tears 
up  trees,  often  removing  them,  and  even  other  heavy  bodies, 
to  a  considerable  distance,  and  by  thunder  and  lightning,  with 
torrents  of  rain  and  hail. 

591.  The  passage  of  highly  electrified  clouds  is  sometimes  attended  by 
the  production  of  singular  phenomena  in  springs  and  fountains  which  have 
their  origin  deep  beneath  the  surface.    The  waters  of  well-known  springs 
have  been  made  to  gush  forth  in  unusual  and  extraordinary  abundance ; 
and  in  some  instances  fissures  have  been  formed  and  streams  issued  where 
none  had  ever  before  been  seen. 

592.  The  Aurora  Borealis. — This    name,   which    signifies 
Northern  Morning,  is  applied  to  luminous  appearances  which 
are,  in  clear  weather,  often  seen  at  the  north,  soon  after  sun- 
set, ox  later  in  the  night.    Sometimes  they  are  presented  in  the 
form  of  a  diffused  white  cloud,  but  more  frequently  they  con- 
sist of  luminous  rays  of  various  colours,  issuing  in  various  di- 
rections, but  always  converging  to  the  same  point.   These  rays 
are  not  permanent,  but  constantly  change  their  position  in 
every  possible  manner,  sometimes  presenting  an  appearance 
like  the  graceful  folds  of  a  riband  or  flag  agitated  by  the  wind, 
as  represented  in  figure  284,  and  then  dividing  into  several 


Fig.  284. 

parts,  and  forming  beautiful  curves  of  light,  enclosed  one  within 
another,  figure  285.     Sometimes,  in  New  England  and  places 

Quest.  590.  What  are  land-spouts  ?  With  what  are  they  usually  attended  ? 
592.  What  is  the  Aurora  Borealis  ?  What  do  they  sometimes  consist  of? 
Do  they  frequently  change  their  appearance  ? 


ELECTRICITY.  301 


Fig.  285. 

farther  north,  the  whole  heavens  are  lit  up  with  them,  which, 
for  hours,  or  even  during  the  entire  night,  continue  to  flash  in 
svery  direction. 

593.  The  mode  in  which  this  phenomenon  is  produced  has 
not  yet  been  fully  established,  but  enough  is  known  to  prove 
conclusively  its  electrical  origin.    The  streams  of  auroral  light 
In  every  part  of  the  heavens  always  tend  towards  the  same 
point  which  is  indicated  by  the  direction  of  the  south  pole  of  the 
dipping-needle  (§  523) ;  here  they  are  often  seen  to  unite,  forming 
a  beautiful  arch  or  corona.    It  is  well  known,  also,  that  during 
the  occurrence  of  the  aurora  the  magnetic  needle  is  usually 
more  or  less  affected,  sometimes  oscillating  through  several 
degrees.    From  the  established  connection  between  electricity 
and  magnetism,  (for  the  discussion  of  which  see  the  author's 
work  on  Chemistry,)  this  is  just  what  should  be  expected, 
considering  this  phenomenon  to  be  produced  by  electricity 
by  some  means  put  in  motion  in  the  upper  regions  of  the 
atmosphere. 

594.  A  popular  notion  has  very  extensively  prevailed,  that 
the  aurora  borealis  was  entirely  unknown  to  the  ancients, 
and  has  been  seen  only  in  modern  times ;  and  some  writers 
of  no  little  merit  have  given  countenance  to  the  error.    This 
has,  no  doubt,  been  occasioned  by  the  fact  that  its  occur- 
rence with  sufficient  brilliancy  to  attract  attention  has  been 
at  very  irregular  intervals,  it  sometimes  disappearing  entirely 

Quest.  593.  Has  it  been  fully  proved  how  they  are  produced  ?  Is  it  cer- 
tain they  are  of  electrical  origin  ?  Towards  what  point  in  the  heavens  do 
the  streamers  of  light  always  tend  ?  What  is  often  formed  in  this  point  ? 
What  is  frequently  the  effect  of  the  aurora  upon  the  magnetic  needle? 
Should  this  be  expected  from  the  known  connection  between  electricity  and 
magnetism,  considering  the  aurora  as  the  effect  of  electricity  in  the  upper 
regions  of  the  atmosphere  ?  594.  What  is  said  of  the  popular  notion  that 
has  prevailed  that  the  aurora  borealis  has  been  seen  only  in  modern  times  ? 

26 


302  NATURAL    PHILOSOPHY. 

for  scores  of  years,  or  even  centuries.  But  instances  of  its  oc- 
currence are  recorded  by  Aristotle,  Cicero,  Pliny,  and  others ; 
and,  between  the  years  A.  D.  583  and  1751,  it  is  said,  it  is 
alluded  to  in  history  as  having  been  seen  no  less  than  1441 
different  times. 

Thermo-electricity,  or  electricity  developed  by  change  of  temperature 
in  certain  cases,  and  also  that  branch  of  the  science  of  electricity  called 
galvanism,  with  its  important  connections  with  magnetism,  are  discussed 
in  detail  in  the  author's  edition  of  Turner's  Chemistry,  to  which  reference 
has  already  several  times  been  made. 

Were  they  seen  by  the  ancients  ?  How  many  times  is  it  said  to  be  men- 
tioned in  history  as  having  occurred  between  the  years  A.  D.  583  and  1751  ? 


THE    END, 


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